Economic Studies 108

David KjellbergExpectations, Uncertainty, and Monetary Policy

David Kjellberg

Expectations, Uncertainty, and Monetary Policy

Department of Economics, Uppsala University Visiting address: Kyrkogårdsgatan 10, Uppsala, Sweden Postal address: Box 513, SE-751 20 Uppsala, Sweden Telephone: +46 18 471 11 06 Telefax: +46 18 471 14 78 Internet: http://www.nek.uu.se/ _____________________________________________________________________ ECONOMICS AT UPPSALA UNIVERSITY The Department of Economics at Uppsala University has a long history. The first chair in Economics in the Nordic countries was instituted at Uppsala University in 1741. The main focus of research at the department has varied over the years but has typically been oriented towards policy-relevant applied economics, including both theoretical and empirical studies. The currently most active areas of research can be grouped into six categories: • Labour economics • Public economics • Macroeconomics • Microeconometrics • Environmental economics • Housing and urban economics ______________________________________________________________________ Additional information about research in progress and published reports is given in our project catalogue. The catalogue can be ordered directly from the Department of Economics. © Department of Economics, Uppsala University ISBN 978-91-85519-15-6 ISSN 0283-7668

Doctoral dissertation presented to the Faculty of Social Sciences 2007

Abstract KJELLBERG, David, 2007, Expectations, Uncertainty, and Monetary Policy; Department of Economics, Uppsala University, Economic Studies 108, 132 pp., ISBN 978-91-85519-15-6. This thesis consists of four self-contained essays: Essay 1 - To evaluate measures of expectations I examine and compare some of the most common methods for capturing expectations: the futures method which utilizes financial market prices, the VAR forecast method, and the survey method. I study average expectations on the Federal funds rate target, and the main findings can be summarized as follows: i) the survey measure and the futures measure are highly correlated; the correlation coefficient is 0.81 which indicates that the measures capture the same phenomenon, ii) the survey measure consistently overestimates the realized changes in the interest rate, iii) the VAR forecast method shows little resemblance with the other methods. Essay 2 - This paper takes a critical look at available proxies of uncertainty. Two questions are addressed: (i) How do we evaluate these proxies given that subjective uncertainty is inherently unobservable? (ii) Is there such a thing as a general macroeconomic uncertainty? Using correlations, some narrative evidence and a factor analysis, we find that disagreement and stock market volatility proxies seem to be valid measures of uncertainty whereas probability forecast measures are not. This result is reinforced when we use our proxies in standard macroeconomic applications where uncertainty is supposed to be of importance. Uncertainty is positively correlated with the absolute value of the GDP-gap. Essay 3 - The co-movements of exchange rates and interest rates as the economy responds to shocks is a potential source of deviations from uncovered interest rate parity. This paper investigates whether an open economy macro model with endogenous monetary policy is capable of explaining the exchange rate risk premium puzzle. When the central bank is engaged in interest rate smoothing, a negative relationship between exchange rate changes and interest differentials emerge for realistic parameter values without assuming an extremely large and variable risk premium as done in previous studies. Essay 4 - This paper shows how market expectations as a function of the forecasting horizon can be constructed and used to analyse issues like how far in advance monetary policy actions are anticipated and how the market’s understanding of monetary policy has developed over time. On average about half of a monetary policy action is anticipated one month before a policy meeting. The share of fully anticipated FOMC policy decisions increase from less than 10% at the two-month horizon, to about 70% at the one-day horizon. The market ability to predict policy has improved substantially after 1999 as the fraction of fully anticipated meetings has quadrupled at the monthly horizon. This improvement can be described as an effect of increased central bank transparency.

Acknowledgement Writing a Ph.D. thesis is easy. All you need is a great deal of interest in the subject, an analytical sense, stamina, stubbornness, time, no urge for 9-to-5-work, patience, a structured mind, open for accepting critique, a liking to sit in front of a computer day in and day out, a private life that does not take too much time and effort, and finally, a liking of the academic procedures. Easy.1 But sometimes you will be in great need of assistance from various persons.

Parts of this thesis have been written together with other economists at the department. My first co-writing project was with Erik Post, a fellow Ph.D. student. I want to thank Erik for many great times and great co-working. Your energy and ability to think out of the box is inspiring, and combined with me as a devil’s advocate I believe we learned a lot.

My second co-writing project was initiated by Annika Alexius, my thesis advisor. She had a very interesting project that needed some extensive simulation programming that I got to put my teeth in. I really enjoyed the project and I am grateful for the opportunity to work with it. As an advisor Annika is as straightforward as she is helpful. She also cares about the person behind the Ph.D student. When I got neck pains she immediately told me to skip work, go home to rest, and to make an appointment with a physiotherapist. Thank you Annika for all your help and guidance.

Another important person that has helped me a great deal is Nils Gottfries, my co-advisor. Nils is the ‘thinker’, helping me to really contemplate what exactly my projects are about. This typically means four to five hour marathon meetings. Although tedious, these meetings have been helpful in many, many, ways. Nils and Annika is a splendid combination of advisors for a Ph.D. candidate in macroeconomics (Post, 2007).

I would also like to thank all of those who have helped me with suggestions and comments when I have presented my papers at seminars. I am particularly grateful to 1 [Dictionary Definition]: ‘Irony [Latin ‘ironia’, Greek ‘eironeia’ simulated ignorance, from ‘eiron’ dissembler]: dissimulation, pretence; especially the pretence of ignorance practised by Socrates as a step towards confuting an adversary.’ (Oxford Dictionary).

Ethan Kaplan who was the discussant for my licentiate paper and Matthew Lindquist who was the discussant at my final seminar.

For the practical matters our administrative staff has solved many of my headaches. Greetings to Katarina Grönvall, Monika Ekström, Ann-Sofie Wettergren-Djerf, Åke Qvarfort, Eva Holst and Berit Levin. Tomas Guvå needs a special mentioning for the cheerful chats in the corridor.

The working environment is especially important when writing a thesis. Here at the economics department in Uppsala we have been a great gang of Ph.D students and Ph.D.’s. First of all I would like to thank my office mate Carl. We have shared the same office for more than five years and have gotten to know each other quite well during these years. And since we both have had a bias for coming in late and going home late, we have had a non-standard lunch hour at 1pm. Those lunches have been both calorie rich and rich of different discussion subjects. To all my friends at the department, thanks for all the good times and ”fika”-moments. Some of you are Erik (Ma-fred!), Fredrik, Christian, Jon, Lars (LAL), Martin Å, Martin S, Jonas L, Jovan, Jakob, Jenny (barnens vän), Elly-Ann, Erika, Karin, Mikael, Hanna, Per and Cecilia. And to the Secret Society of Steaks, you know who you are.

During these years as a Ph.D. student I have been heavily engaged in the Swedish pinball community. It has helped me to relax after periods of intense Ph.D.:ing. To all my friends in the pinball hobby: “LDK - is here to play”.

During the last year I have gotten to know Karolina. You have made my days brighter. Hopefully, finishing this thesis will allow me to spend even more time with you in the future.

John, you are my brother and one of my best friends. Thank you for being so cool. Mamma och Pappa, you have always supported my choices in life. I am so grateful for being your son. This thesis would not have been possible without your support.

When I started my Ph.D. studies it felt like one of the big goals in my life. Five years later I still feel that this was one of the things I really wanted to experience and achieve. I am very happy I got to write this thesis and I have enjoyed it a lot.

David “LDK” Kjellberg

Uppsala, October 2007

Contents

Introduction ...................................................................................................... 1

References ................................................................................................. 7

Essay 1

Measuring Expectations................................................................................... 9

1 Introduction......................................................................................... 11

2 Methods for Measuring Expectations ................................................. 14

2.1 VAR Forecast Method............................................................ 15

2.2 Futures Method....................................................................... 17

2.3 Survey Method ....................................................................... 20

3 Data ..................................................................................................... 23

4 Comparing the Measures of Expectations .......................................... 24

4.1 Descriptive Statistics .............................................................. 24

4.2 Autocorrelations ..................................................................... 35

4.3 Correlations between Measures.............................................. 36

5 Conclusions......................................................................................... 45

References ............................................................................................... 47

Data Appendix ........................................................................................ 49

Essay 2

A Critical Look at Measures of Macroeconomic Uncertainty ................... 51

1 Introduction......................................................................................... 53

2 A Model Motivation............................................................................ 55

3 Uncertainty Proxies............................................................................. 57

3.1 Stock Market Volatility .......................................................... 58

3.2 Disagreement Proxies ............................................................. 59

3.3 Probability Forecast Proxies ................................................... 60

4 Do Uncertainty Proxies Measure Uncertainty? .................................. 60

4.1 Narratives................................................................................ 60

4.2 Correlations ............................................................................ 65

5 Factor Analysis ................................................................................... 66

6 Extensions ........................................................................................... 70

6.1 Co-movements with the Business Cycle ................................ 70

6.2 Precautionary Savings ............................................................ 72

6.3 Residential Investment ........................................................... 73

7 Conclusions......................................................................................... 74

References ............................................................................................... 76

Essay 3

Can Endogenous Monetary Policy Explain the Deviations from UIP?..... 79

1 Introduction......................................................................................... 81

2 The Puzzle........................................................................................... 83

3 The Model ........................................................................................... 84

4 Calibration........................................................................................... 86

5 Deviations from UIP in Simulated Data ............................................. 88

6 Impulse Response Functions............................................................... 93

7 Decompositions of the Deviations from UIP...................................... 95

8 Second Moments in Simulated Data ................................................... 98

9 Conclusions....................................................................................... 100

References ............................................................................................. 102

Essay 4

Analyzing Unexpected Monetary Policy .................................................... 105

1 Introduction....................................................................................... 107

2 Measuring Market Expectations ....................................................... 109

3 Data ................................................................................................... 112

4 Expectation Formation as a Function of Forecast Horizon............... 112

4.1 Market Expectations on Scheduled FOMC Meetings .......... 113

4.2 Excluding Overlaps .............................................................. 119

4.3 FOMC Meetings with and without Action ........................... 121

5 Measuring Impact of Improved Transparency.................................. 125

6 Conclusions....................................................................................... 129

References ............................................................................................. 131

Introduction The thesis consists of four independent essays relating to the subject of expectations in macroeconomics. This introduction presents a brief background to the subject and an overview of my work.

The concept of expectations is a crucial component of modern macroeconomic theory. For instance, consumption, investments and savings decisions are all functions of expected future cash flows and expected future discount factors. Asset prices are also determined by expected future outcomes. There are numerous examples of how important the concept of expectations is in economics, and macroeconomics in particular. To put it simply, expectations about economic variables have a decisive impact on most types of economic actions and decisions.

In a mathematical-economical framework we think of the agent’s expectations about a variable x as a conditional expectation, which depends on all relevant information currently available. If you are expressing your expectation about the value of x in the upcoming period, t+1, we typically designate that value as

E(xt+1|Ωt),

where Ωt denotes all relevant information at time t. Still, this expression only contains the expected mean of x; we can extend the agent’s expectations to include the whole distribution of xt+1. An expected distribution of xt+1 typically implies that the agent has formed an opinion about all possible outcomes of xt+1, as well as the probability for each outcome. We can illustrate an expected distribution of x as a probability density function, as depicted in Figure 1.

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Figure 1 An Expected Outcome Distribution of x

E(x)

Again, the mean of the expected distribution is the expected value E(xt+1). The shape and spread of the distribution describes the expected uncertainty regarding the possible outcome of the variable xt+1.

An agent’s true expectation E(xt+1) is rarely, if ever, directly observable to the economists. The true expectations are in the mind of the agent, out of reach for the curious social scientists. In macroeconomics, we are mostly interested in aggregate expectations, i.e. expectations representing the whole cohort of economic agents. This makes it even trickier to measure expectations. Nevertheless, empirical estimates of expectations are used by economists around the world, both by academics and practitioners. Several different measures of expectations have been suggested over time. A few of the most commonly used are: survey answers, econometric forecasts, economic model forecasts, and forecasts based on financial market prices. Initially, it would seem that the measures of expectations were suggested after thinking: “better a bad measure of expectations than no measure at all”. Lately, with the introduction of better surveys and more sophisticated measures based on market prices of financial derivates (e.g. see Söderlind and Svensson, 1997; Gürkaynak and Wolfers, 2006) the search is much more focused on finding the “most correct” measure of expectations.

The essays in this thesis deal with different aspects of aggregate expectations and aggregate uncertainty in macroeconomics, with both methodological and applied agendas. An agent’s views about the mean and the distribution of a future outcome are inherently unobservable. Still, we often have to impute a proxy for these variables. The first two essays focus on methods for evaluating measures of expectations and

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uncertainty. The third essay proposes a model consistent solution to the well known exchange rate risk premium puzzle where expectations about future exchange rate movements play a crucial role. The last essay uses financial market prices to derive expectations on monetary policy for different forecast horizons and demonstrate how these can be used to evaluate central bank transparency.

In Essay 1 I present an approach to how we can evaluate different measures of expectations given that true expectations are unobservable. The future target rate of the Federal Reserve serves as a convenient object to study when it comes to measures of expectations, because so many of the different methods are available in this particular case. Questions about the Federal funds rate are included in several surveys and there are also well developed futures markets for this interest rate. The idea behind survey data is simply to ask people what they believe about future interest rates, while agents actually put the money where their mouth is when they buy and sell financial assets. A third measure of expectations stems from statistical forecast models. The paper compares these three fundamentally different measures of expectations.

I claim that if we find two different types of measures that have similar time series properties and, most important of all, are highly correlated, they are very likely to both measure the unobservable true expectations. The key to making this claim is that because the correlated measures are fundamentally different, any measurement errors must be orthogonal to each other and cannot be causing the correlation.

In this essay I demonstrate the evaluation approach by comparing three specific and fundamentally different measures of expectations on Federal funds rate target: a simple time series forecast model (a VAR-model type of equation), a survey measure, and a market based measure (derived from a futures contract price). The results indicate that the baseline measure, the time series forecast, does not forecast the Fed target rate well. Furthermore, the time series forecasts are not strongly correlated to the other two types of measures, even though some specifications show correlation coefficients of about 0.30. The central result from this essay is that the survey and the market measures are highly correlated. They also show similarities in their time series properties. The conclusion is that the survey and the market based measure are able to pick up the true aggregated expectations on the Fed target rate. Both measures can have some measurement errors, but these are not serious enough to distort the underlying measurement of the expected target rate.

A measure of expectations is often required in empirical macroeconomics. Surprisingly little is known about different types of measures that figurate in the literature. This paper shows how they can be evaluated and also indicates that survey

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measures and expectations derived from financial futures prices are more appropriate than measures based on time series methods.

In Essay 2 (with Erik Post), we investigate different measures of macroeconomic uncertainty. As discussed above, uncertainty is typically described as the width of the expected distribution of the variable outcome x. If the aggregate expected distribution of x is wide, the market sees a lot of probable outcome scenarios, indicating that the market is uncertain about what the outcome will be.

Macroeconomic uncertainty is a wide definition of uncertainty, here symbolizing a general sense of unclear economic future. We do not claim to be able to measure this uncertainty with one single variable, but rather study the uncertainty of a wide variety of individual macro variables.

If conditional expectations are difficult to measure, conditional uncertainty is even worse. With expectations we at least have an outcome to evaluate against, but with conditional uncertainty there is no ex post outcome. In this essay we introduce a narrative evaluation method to allow us to assess different measures of macroeconomic uncertainty. This narrative method suggests that an appropriate measure of uncertainty should respond to exogenous events of uncertainty, as for instance events of war or terrorist acts, but also the reduction of uncertainty after a U.S. election is decided. This idea is supported by for instance Bloom (2006), who finds a substantial increase in the use of the word “uncertainty” for the Federal Open Market Committee meetings after the terrorist attacks of 9/11. We find several proxies of uncertainty that react on this type of exogenous events, but we also find that one of the more theoretically appealing measures fail to react.

The essay also addresses the question whether different types of macroeconomic uncertainty proxies are correlated. We find two distinct groups of proxies where the measures are correlated within the group, but not between the groups. One of the groups contains survey measures of uncertainty, describing the disagreement among the respondents regarding the level expectations. The uncertainty measures of this group are based on a variety of macroeconomic variables and by performing a factor analysis on them we conclude that all these different measures have only one common factor. Presumably this driving factor is representing some kind of general uncertainty affecting most macroeconomic uncertainty variables.

Finally, we take the main types of uncertainty proxies to some applications to study the correlations with business cycle, consumption, and housing investments. The proxies are positively correlated with the absolute value of a GDP-gap measure, indicating that uncertainty increases around the turn of the business cycle. We also find that the proxies have some explaining power for both consumption and housing

4_____________________________________________________________________________________Introduction

investment, again validating the proxies’ ability to capture (macro)economically important uncertainty.

Essay 3 (with Annika Alexius) deals with what is known as the exchange rate risk premium puzzle. The UIP hypothesis states that the interest rate differential between two countries should reflect the expected exchange rate change so that the expected returns to investments in bonds denominated in the two currencies are equalized. The empirical results, however, have shown little or no support for the UIP-relation to hold. In fact, the empirical estimates often indicate that the exchange rate movements are the opposite of the UIP prediction.

One possible explanation for the puzzle is the existence of a large and highly variable risk premium in the exchange rate. However, endogenous models of the exchange rate risk premium have failed to generate premia of the required magnitude. McCallum (1994) suggests that the negative co-movement between exchange rate changes and interest rate differentials could be a consequence of the monetary policy responds to shocks to the economy. Our approach is to use an open-economy macro model with monetary policy, by Svensson (2000), to create simulated time series of the exchange rate and the interest rate differential. By performing the empirical UIP-test on the simulated data, we investigate if we can find parameterizations of the model where the UIP-test yields the same contradicting results as the true data do. The results of this exercise reveal that if the model is calibrated to make the monetary policy more effective, making the interest rate differential less volatile, the UIP puzzle can be found in simulated data. In particular, if we introduce a preference for interest rate smoothing in the central bank’s loss function, the observed negative relationship between exchange rates and interest rates can be obtained from the model using realistic parameter values.

Essay 4 presents an approach for evaluating the development of market expectations over time, as an event approaches. As in Essay 1, I study the expectations on monetary policy before Federal Open Market Committee meetings. By plotting the average absolute expectations errors against the forecast horizon we can discover at what pace the market expectations improve as the policy meeting approaches. Using the Federal funds futures rate we can also estimate if a meeting outcome was anticipated by the market participants, and at what horizon the expectations lined up with the outcome. I present plots of how the number of anticipated meetings changes with the forecast horizon, and how this time relation has changed in recent years. Expectations are also much more correct concerning policy meetings where the target interest rate is left unchanged than when the Federal Reserve actually implements changes.

Swanson (2004), Poole and Rasche (2000), among others, have shown how Fed transparency, e.g. their communications of policy intentions, has improved expectations

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on Fed policy since 1994 when the Fed changed their policy announcement procedures. Hamilton (2007) suggests that the transparency has improved even further after 1999 and refers to descriptive statistics of Fed futures rate. However, Ehrmann and Fratzscher (2005) investigate the difference in the immediate surprise between the two samples 1994-1999 and 2000-2004 and find that the market expectations have not improved in any significant way since 1999. Using the method introduced in this essay I can study how the expectations change gradually during two months prior to a FOMC meeting. Ceteris Paribus, smaller average expectation errors across horizon implies higher transparency. In contrast to the results of Ehrmann and Fratzscher (2005), my findings indicate that the market anticipates the policy decisions much earlier during the period 2000-2006, compared to the period 1994-1999. This exemplifies how the evaluation approach can be used to study transparency over time.

6_____________________________________________________________________________________Introduction

References

Bloom, Nicholas, “The Impact of Uncertainty Shocks: Firm Level Estimation and a 9/11 Simulation,” Discussion Paper 718, Center for Economic Performance, London School of Economics, March 2006.

Ehrmann, Michael and Marcel Fretzscher, “Transparency, Disclosure, and the Federal

Reserve”, International Journal of Central Banking 3 (1), March 2007, p. 179-225.

Gürkaynak, Refet S., and Justin Wolfers, “Macroeconomic Derivatives: An Initial

Analysis of Market-Based Macro Forecasts, Uncertainty and Risk”, Working Paper Series 2005-26, Federal Reserve Bank of San Francisco, 2005.

Hamilton, James D., “Daily Changes in Fed Funds Futures Prices”, NBER Working

Papers 13112, National Bureau of Economic Studies, May 2007 (Forthcoming in Journal of Money, Credit and Banking).

McCallum, Benneth, "A Reconsideration of the Uncovered Interest Parity

Relationship", Journal of Monetary Economics 33 (1), February 1994, p. 105-132. Poole, William, and Robert H. Rasche, “Perfecting the Market’s Knowledge of

Monetary Policy”, Working Papers 2000-010, Federal Reserve Bank of St. Louis, December 2000.

Swanson, Eric, “Federal Reserve Transparency and Financial Market Forecasts of

Short-Term Interest Rates”, Finance and Economic Discussion Series 2004-06, Board of Governors of the Federal Reserve System, February 2004.

Svensson, Lars E. O., "Open-Economy Inflation Targeting," Journal of International

Economics 50 (1), February 2000, p. 155-183. Söderlind, Paul and Lars E. O. Svensson, ”New Techniques to Extract Market

Expectations from Financial Instruments”, Journal of Monetary Economics 40 (2), October 1997, p. 383-429.

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Essay 1

Measuring Expectations

1 Introduction Expectations play a vital role as one of the basic building blocks of theoretical macroeconomic models. To correctly measure the empirical expectation on an economic variable is difficult since we cannot directly observe the true expectations of the agents in the economy. The true expectations exist in our minds, sometimes only as a feeling, and to consistently retrieve them from there seems like an impossible mission. This problem is particularly evident when we deal with aggregate market expectations, which is typically the case in macroeconomics. Hence, it is difficult to evaluate the methods used to measure expectations – there are no true expectations to which the measures can be compared. Despite all these problems, various methods are being used to measure expectations, simply because there is no way around including empirical estimates of expected variables in macroeconomic models.

There are many macroeconomic topics where aggregate expectations play a crucial role. Estimates of the Phillips curve, as for instance in Akerlof et.al. (2000), rely heavily on empirical estimates of inflation expectations. Another important area where inflation expectations are important is the estimation of the real interest rate (e.g. Lai, 2004). We can also use a measure of expectations to compute the surprise component, the shock, when an official macro variable is announced. The economic impact of different shocks has been studied in both financial and macroeconomic settings. Empirical financial studies frequently investigate how the returns on asset investments are affected by macroeconomic shocks (e.g. Bernanke and Kuttner, 2005), while macroeconomic studies often tend to focus on monetary policy transmission effects (e.g. Kuttner, 2001 or Gürkaynak, 2005). Expectations are important in economic decision making, and both policy makers and economists would benefit from a better knowledge about how to measure the true expectations.

In this paper I study three different methods which are commonly used to measure expectations empirically: the futures method, the survey method, and the VAR forecast method. The futures method derives market-based expectations implicitly from prices of traded futures contracts. The survey method measures expectations by asking a sample of people what they expect about a variable. The VAR forecast method estimates a VAR-model and uses the out-of-sample forecasts of the model to proxy expectations of the variables. By comparing these three methods with each other, and with the realized outcome of the variable, we can observe if the measures confirm or contradict each other.

The expectations studied in this paper are the expectations on the Federal funds rate target (FFRT). The FFRT is controlled and used by the Federal Reserve Bank (Fed)

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to implement U.S. monetary policy, and it is an important macroeconomic and financial variable that is monitored by markets all over the world. The FFRT is a suitable variable for this kind of investigation since we can readily measure expectations of it with the futures method, the survey method and the VAR forecast method.

The expectations measures here refer to relatively short horizons, from expectations one day ahead up to expectations one month ahead. Expectations for such short time periods should have relatively small error components compared to expectations for longer time periods, and with less noise it should be easier to make fair comparisons of the different methods. The choice of horizon is also due to the nature of the data since the highest available frequency for the survey and the VAR variables is a monthly frequency.

To make sure the different methods measure the same expectations, I try to define them in such a way that they are conditioned on the same information set. The measures are then compared and analyzed in various ways. Descriptive statistics and autocorrelation patterns are discussed, forecasting properties are investigated and the measures are plotted against each other, together with correlation tests. While previous studies have mainly been interested in forecasting ability, I am more interested in analyzing similarities and differences between the measures. The true expectations are not necessarily good forecasts, which makes it appropriate not to focus too much on forecasting efficiency. The three approaches to measuring expectations differ fundamentally and finding strong similarities between the measures would indicate that they capture the same underlying phenomenon – most likely the true expectations. Each method has a different and theoretically plausible link to the true expectations. If we have accurate measures of expectations, we expect high correlations between these measures. A high correlation coefficient could also be due to correlated measurement errors, but since the methods are fundamentally different the measurement errors for each measure should be independent from one another.

The data material in this study covers the time period 1994 to 2004 and contains 88 scheduled Federal Open Market Committee (FOMC) meetings. Data for the statistical method, the VAR-model, is mainly collected from the real-time data supplied by the Federal Reserve Bank of Philadelphia. The futures method data are quotes from the Chicago Board of Trade, supplied through Hansson & Partners AB. The survey method makes use of the Michigan Consumer Survey.

Several studies have evaluated measures of expectations. Most of them investigate one measure at a time and focus on unbiasedness only, which is a critical test of rational expectations. Some studies suggest that the futures method of extracting expectations is an unbiased and appropriate measure of expectations for the FFRT, from a rational

12_____________________________________________________________________________________Measuring Expectations

expectations point of view (see Söderström, 2001; Kuttner, 2001; Gürkaynak et. al., 2002). The futures measure has been used as a benchmark for the true expectations, by e.g. Evans and Kuttner (1998) and Durham (2003). The available evidence on the survey method is unclear, depending very much on the particular variable in focus. For instance, the Money Market Services (MMS) survey has generally been found to have reasonable properties as a measure of expectations. For most variables it is unbiased and outperforms naive time series forecasts (Balduzzi et. al., 2001). Gürkaynak and Wolfers (2005) show that the MMS survey results for a couple of common macroeconomic variables have similar forecasting properties as a newly introduced market based measure of expectations derived from “economic derivatives”. However, Faust et.al. (2003) claim that the MMS survey does not pass the basic tests of unbiasedness for FFRT expectations. The VAR-model for monetary policy has been criticized by Rudebusch (1998) and Evans and Kuttner (1998) for having bad FFRT forecasting properties. These two studies also make a simple comparison between the surprise changes in FFRT derived from VAR forecasts and the futures method, and they find a low correlation between these two measures. Evans and Kuttner (1998) do find a higher correlation between the derived surprise factors when they modify the specification of the VAR-model. However, they also point out a weakness in only studying the correlation between the surprise factors, since this correlation is affected by the non-relevant sample correlations between each of the expectations measures and the FFRT change. In this study I do not focus on the surprise factor, but instead evaluate different characteristics of the measures of expected changes in FFRT.

Previous studies of measures of expectations do not thoroughly compare the different approaches. Hence, this paper contributes to the existing literature by performing a systematic comparative analysis of the methods. I investigate to what extent different measures of expectations capture the same underlying phenomenon and try to evaluate whether they pick up the unobservable true expectations. The main finding is that the expected interest rate changes as measured by the survey method and the futures method are highly correlated. The survey estimate of expectations overestimate expected changes relative to the true outcome as well as relative to the expectations derived from federal funds futures. Hence the survey measure is biased, in a forecasting sense, with high forecasting errors in comparison to the other methods. Except for the mean bias of the survey method, these two fundamentally different ways of measuring the same expectations yield surprisingly similar estimates. The high correlation indicates that the futures method and the survey method most likely are measuring the true expectations in a fairly accurate way. The VAR forecast methods,

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however, generate quite different estimates of the expectations for the FFRT compared to the survey and futures methods.

The rest of the paper is organized as follows. In section 2 I describe the different methods for measuring expectations and section 3 describes the data material. Section 4 presents and analyses the empirical results. Section 5 concludes.

2 Methods for Measuring Expectations The VAR forecast method, the futures method and the survey method are completely different in their approach to measuring expectations. The VAR forecast method uses econometric model forecasts of the FFRT to proxy the expected outcome of the target rate. The futures method derives implicit expectations from the market price of the Federal funds rate futures. There are several surveys that include questions concerning what the respondents expect about the future changes in the target rate. These methods are here applied to the practical problem of estimating the expected FFRT change for each scheduled FOMC meeting, which are the meetings that decide if the Fed will change the target rate or not. The meetings are scheduled eight times per year, with approximately six weeks between each meeting.1

To make the comparison of expectations measures as exact as possible we need to equalize the information sets that the different measures are conditioned on. This is not trivial since the three methods are fundamentally different and are not fully comparable in the sense that they use the information available on exactly the same point in time. I let the measures be conditioned on information available at the end of the month previous to the FOMC meeting month. Since the meetings can be scheduled to take place during any weekday of a month, the theoretical expectations horizon then varies between one and 31 days. The futures method can easily be pinpointed to an exact day, which is chosen to be the last trading day of the month prior to a FOMC meeting. The VAR forecast method includes data theoretically available at the first day of the meeting month. The survey method uses survey data that was collected during the month prior to the corresponding FOMC meeting. The information sets of the methods cannot be perfectly equalized, but the difference between them is made as small as possible.

Below I discuss the methods and the calculation procedures for each measure. I also explain how each measure can be interpreted as a measure of the true expectation.

1 In turbulent times there can be unscheduled meetings in between the scheduled meetings.

14_____________________________________________________________________________________Measuring Expectations

2.1 VAR Forecast Method

Time series models are often used as forecasting tools. By using historical time series data we can estimate statistical relations and use the most recent data to form a forecast. This forecast can be seen as an expectation if agents have access to the same information set that is included in our econometric model.

Forecasting monetary policy has been the subject of many empirical studies. One of the most common statistical approaches is to set up a VAR-system.2 The only equation of interest for our purpose in the VAR is the FFRT-equation, which uses lagged values of FFRT and other macroeconomic variables as independent variables, typically using monthly data. There are several suggestions as to what variables should be included in the VAR. Christiano, Eichenbaum and Evans (CEE) (1996) describe what can be called a benchmark model for Monetary Policy VAR on monthly data.3 They set up a seven variable VAR in levels with twelve lags. The CEE-VAR is one of the two VAR-models used to make VAR forecasts of the FFRT in this paper:

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iitit

uMTRNBR

GSCICPINFFRFFR

++++

++++=

∑∑∑

∑∑∑∑

=−

=−

=−

=−

=−

=−

=−

βββ

βββββ (1)

To avoid the discrete steps of FFRT the market traded FFR is used instead.4 The other variables in this regression are payroll employment (N), Consumer Price Index (CPI), the growth rate of Goldman & Sachs Commodity Price Index (GSCI), non-borrowed reserves (NBR), total reserves (TR) and the monetary aggregate M1.5 All variables are in logs and real-time values, e.g. the CPI-value for November 2004 is the number

2 This is often used to study the effects of monetary policy shocks on other economic variables by using impulse-response functions. Here I am not interested in the monetary shock element but the whole innovation in FFRT changes. 3 The CEE VAR is used in for instance Rudebusch (1998), Evans and Kuttner (1998), and Robertson and Tallman (1999). It can be seen as a representative benchmark model for a large part of the sample period 1994 to 2004. 4 The monthly FFR variable is in fact an average over the daily FFR market quotes during a specific month. 5 These variables (except GSCI) all have long trends and are typically non-stationary when tested for a unit root. The commodity price index (GSCI) and regular price index (CPI) variables are not the same as used in Christiano, Eichenbaum and Evans (1996). Since the original series are either discontinued or not publicly available they had to be replaced by equivalent variables.

_____________________________________________________________________________________15

presented in the beginning of December 2004 and not a revised value presented several months later.

I first use the CEE-specification to produce out of sample forecasts of the FFRT.6 The difference between the forecasted level of FFRT and the current FFRT gives the expected change of FFRT. I tried alternative specifications with first differenced variables, shorter lag lengths and fewer variables, but the qualitative results are generally the same as for the CEE-specification.7 An exception was the specification with three lags of first differenced CEE-variables. This alternative specification gives interesting differences in the estimates of the expectations compared to the CEE-VAR. Therefore, both the standard CEE-VAR and this alternative VAR, named ALT-VAR, will be reported for comparison with the other two methods.

To get a VAR forecast measure of the expected change of FFRT to be comparable to the data for the futures and survey method, the forecasts start in the beginning of 1994. Using the first estimate of the VAR-coefficients and the current VAR-variables we can forecast the FFRT of January 1994. The data used to estimate the VAR-models covers January 1985 up to the date of the forecast, i.e. the sample period will increase with time.8 Forecasts are constructed for all months from January 1994 up until June 2004, covering the selected sample period for FOMC meetings. For every month I re-estimate the VAR-model, using the updated information set, and then make a forecast of the FFRT for the upcoming month. I then select all forecasts for months with FOMC meetings and use them as expectations on the decisions about FFRT changes.

For the VAR-approach there are some difficult timing issues when estimating the model and making forecasts for certain FOMC meeting months. For instance, the employment report for the previous month is not announced until the first Friday of the current month, and the value of the CPI is announced the 13th of the current month. This creates forecasting situations where we might have access to last month’s employment but not the CPI level of that month.9 These timing issues are solved by simply assuming the relevant information is available at the start of the month. As a robustness test I check if the VAR measures of expectations are sensitive to this assumption by studying the difference between FOMC meetings that have taken place in the first and last half of 6 I use real-time data instead of revised data, and also a different commodity price variable than Christiano, Eichenbaum and Evans (1996) did. The sample periods are also different. CEE (1996) used data from 1960 to 1992, while I am using data from 1985. Any attempts to reproduce the CEE-results would be futile with all these differences in data. 7 I tried VAR-estimations with lag lengths of three and twelve lags, variables in levels and first differences, with three variables (FFR, N, and CPI) and seven variables (the CEE-variables). 8 I also tried using a nine year moving time band of data, throwing out the oldest observation as a new observation is added, but this does not change any results or conclusions in the paper. 9 The value of FFRT and GSCI is available immediately after the last month. NBR, TR and M1 are reported every week, much like the employment.

16_____________________________________________________________________________________Measuring Expectations

the month. For the observations made in the last half of a month all information about the previous month is always publicly available and if there is a difference in results compared to the first half of the month it would indicate that the timing is important.10 The difference in the bias test is tested by including dummies on intercept and slope coefficients for the first half of the month. Neither the CEE-VAR or the ALT-VAR shows any significant difference, i.e. the coefficients of the dummies are insignificant.11 This implies that the timing issue seems to have little impact on the qualitative results of the VAR measures.

2.2 Futures Method

The FFRT differs from most macroeconomic variables in that there are financial market prices connected to the FFRT that can be used to derive expectations of future monetary policy. A measurement method based on market prices is intuitively appealing since agents can be said to reveal their true expectations by acting on economic incentives. One of the financial instruments which can be used for this purpose is the Federal funds rate futures contract, traded on the Chicago Board of Trade. From the price of this futures contract we can implicitly derive what the participants on the futures market expect about the FFRT. Gürkaynak et. al. (2002) find that the Federal funds futures dominate other market-based measures of monetary policy expectations, like Eurodollar futures and implied forward rates from various term interest rates. The futures method allows us to estimate very short term expectations, as well as expectations for time periods up to at least six months.12 There are several different derivation techniques available, mostly depending on which horizon the expectations are computed for. The differences are consequences of the construction of the futures contract. A contract’s settlement price is based on the average effective Federal funds rate for the whole settlement month. The averaging needs to be accounted for when we want to derive expectations over time horizons shorter than a month. Another issue is that the futures contracts are based on the effective Federal funds rate and not the target rate itself. The Federal funds rate is the traded market rate that the Fed, by open market operations, keeps close to their stated target rate, the FFRT. The Federal funds rate and the target rate are typically very close, but there are discrepancies that are sometimes quite large;

10 Out of the 87 observations 29 are made in the first half and 58 in the late half of the month. 11 Differences in the point estimates of the correlation coefficients between the VAR-measures of expectations and the futures and survey measures are also small. 12 It might also be possible to use the 12- and 18-month futures contracts to derive expectations for even longer time periods.

_____________________________________________________________________________________17

see Figure 1.13 For longer time horizons there may be a need to adjust futures-based expectations measures for systematic deviations between the effective rate and the target rate, as well as for a possible risk premium in the futures price. These adjustments have been described by Söderström (2001) and Piazzesi and Swanson (2004). Since I use measures with a short term horizon and ex post observations these methods are not applied in my calculations.

Figure 1 Federal Funds Rate vs. Target

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FFRT CHANGE FFR CHANGE

Basi

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ints

The sample contains all FOMC meetings from January 1994 to December 2004. FFR is the Federal funds rate and the FFRT is the Federal funds rate target. The numbers are in basis points.

The derivation technique used in this paper is usually applied to derive

expectations in the very short run, such as one-day-ahead expectations. This method is here extended to derive expectation for horizons up to 30 days. The technical procedure of this derivation is described in Krueger and Kuttner (1996), and in Kuttner (2001).14 Kuttner (2001) calls this particular futures method a “market-based proxy” for expectations on Fed policy. This is an ex post measure, since we need to know the futures price after the FOMC meetings to calculate it. As such it cannot be used as a 13 The correlation coefficient between the FFR and FFRT is 0.998 on monthly data from 1994:1 to 2004:12 and for the first differences of the same variable the coefficient is 0.793. On average there is no significant systematic divergence between changes of FFR and FFRT. However, Söderström (2001) shows there are significant deviations for certain periods that must be accounted for if using the futures rate as an ex ante expectations measure. 14 These references show the derivation of the one day horizon expectation.

18_____________________________________________________________________________________Measuring Expectations

forecasting method, as opposed to the other two methods described in this paper. The advantage of this measure relative to alternative futures measures is that any time invariant risk premium in the futures price, that could distort the futures rate as an expectations measure, is differenced out.15 There are ex ante futures measures, described by e.g. Söderström (2001) and Bernanke and Kuttner (2005), but these definitely need to be adjusted for a possible risk premium and systematic deviations from the target rate (Piazzesi and Swanson, 2004). Such an adjustment could introduce further errors into the measure of expectations. Hence, the ex post futures measure is more appropriate to use in this study.

The Krueger and Kuttner method of deriving the short term market expectation assumes that there is only one Fed decision about the FFRT per month.16 The calculation is quite straightforward; one simply looks at how the spot-month futures rate changes on the announcement day 0

,τsf τ of month s compared to x days before. If

the futures rate is unchanged the Fed action was as expected and the unexpected change is zero. If there is a change in the futures rate we can derive the unexpected change in the target rate for an expectation horizon of x days, u

x iτ~Δ , as

( 0,

0,

~xss

s

sux ff

mmi −−−

=Δ τττ τ), (2)

where is the number of days in the spot-month s.sm 17 This is the measure for the x-day

futures measure of unexpected changes in the FFRT. The expected change can then be derived by using tx i~Δ , the true change in FFRT during the x-day horizon period:

u

txtxe

tx iii ~~~ Δ−Δ=Δ . (3)

I calculate the expected change of the FFRT for all FOMC meetings from the beginning of 1994 to 2004. To measure expectations for approximately the same time horizon as the VAR type of measures, I choose to let the day of the expectation be the last trading day of the month previous to the FOMC meeting. This means x can vary between one

15 The risk premium is considered to change very slowly and only on a longer term, not from day to day according to Piazessi and Swanson (2004). Using the first difference of the futures price to derive the unexpected change in FFRT will therefore not likely be influenced by changes in the risk premium and should not suffer from any significant risk premium bias. 16 Since 1994 there has only been one month where the Fed performed two target rate changes and that was in January 2001. The first change came on the 3rd of January and was the result of an unscheduled meeting. The second change was decided upon at a scheduled meeting, the 31st of January. 17 For a derivation of this formula, see Kuttner (2001).

_____________________________________________________________________________________19

and 30 days. The futures contract I use for a specific expectation calculation is the spot futures contract for the month of the current announcement.

One problem with this particular method is that during the last days of the month, the adjustment for the averaging element goes to infinity, amplifying very small distortions in the futures rate (Kuttner, 2001). The futures measure of expectations on FOMC meetings during the last days of the month is therefore inexact. Kuttner (2001) considers the last three days of the month to be problematic, and therefore I exclude the observations that measure expectations on FOMC meetings taking place during the last three days of the month.

2.3 Survey Method

An obvious method for measuring people’s expectations is to simply ask them what they expect about the outcome of a variable. This method is intuitively appealing since we go straight to the source to measure the expectations. Surveys regarding macroeconomic variables are often in the form of expert surveys, directed at professional forecasters. There are also non-expert surveys directed at larger groups such as consumers or producers. Survey data might seem like an accurate and direct measure, but there are drawbacks. The people participating in a survey might not be representative for all agents of the economy, and this may introduce a bias when measuring aggregate expectations. There is also the possibility of respondents stating an expected value that does not coincide with their true expected value, either on purpose or unintentionally. For instance, Peterson (2001) shows that professional forecasters mimic other forecasters, possibly because they do not want to end up being more wrong than their competitors. Contrary to the futures method, there are no economic incentives for the survey respondents to state their true expectations and this might introduce measurement errors in the survey estimates of expectations (Johansson, 2007).

There are several sources available for survey data regarding expectations about the FFRT. Two well known expert surveys are the MMS survey data and the Blue Chip Financial Forecasts survey data. The MMS survey has asked money managers about their forecasts of several macro variables every week since 1977. The Blue Chip Financial Forecasts is a monthly survey asking financial market experts about their quarterly forecasts of financial variables. A non-expert survey is the Michigan Consumer Survey, which performs a monthly survey about a wide array of topics, one of which is related to the future development of interest rates. The two expert surveys were difficult to obtain in sufficiently long and complete time series, while the

20_____________________________________________________________________________________Measuring Expectations

Michigan Consumer Survey is publicly available on the internet.18 19 Due to these restrictions I use the Michigan Consumer Survey as the survey measure of the expected Fed interest rate policy, despite some drawbacks of that measure that are discussed below.

The survey question asked about interest rates in the Michigan Consumer Survey is: “No one can say for sure, but what do you think will happen to interest rates for borrowing money during the next twelve months – will they go up, stay the same, or go down?”

The Michigan Consumer Survey is a qualitative survey. To be able to compare the survey measure with the other measures of expectations the data has to be quantified. This is done using the Carlson and Parkin (1975) method. Under specific assumptions we can turn the discrete and qualitative response variable into a continuous and quantitative average expectations variable.

There are four possible responses to the survey question: “Up”, “Same”, “Down” and “Don´t know”. The survey data set contains the percentages of the respondents who choose each of these different categories. The first assumption needed to use the quantifying method of Carlson and Parkin (1975) is that a fraction α of the respondents are incapable to form an expectation about future interest rates. This fraction is always classified as “Don´t know”, but does not necessarily exhaust that category. Another assumption is that within a certain boundary above and below zero, the expected change is so small that the respondent answers “Same”. The standard assumption in Carlson and Parkin (1975) is that these threshold values, expressed in percent and designated δ, are symmetric and constant, i.e. the same over time for both positive and negative expected changes.

We also need to make an assumption about the distribution of expectations across the total population. Carlson and Parkin (1975) use the normal distribution in their calculations, but several other suggestions have been used and tested. The differences between the most common distributions are rather small according to Dasgupta and Lahiri (1992), Balcombe (1996) and Mitchell (2002). The normal distribution appears to provide similar estimates of expectations as for instance the logistic distribution or the t-distribution (Mitchell, 2002). For simplicity I choose to use the normal distribution.

18 Another complication is that historical data for the MMS survey is not for sale anymore. Since I have not found a way to legally obtain the MMS survey from any other source I am not able to include it in this paper. 19 http://www.sca.isr.umich.edu/

_____________________________________________________________________________________21

With the assumptions above we can simply insert the data into the Carlson and Parkin (1975) formula to calculate the expected change of the interest rate:20

t

tt

tt

et

PP

PP

i ε

αα

ααδ +

⎟⎟⎠

⎞⎜⎜⎝

⎛

−Φ+⎟

⎟⎠

⎞⎜⎜⎝

⎛

−Φ

⎟⎟⎠

⎞⎜⎜⎝

⎛

−Φ−⎟

⎟⎠

⎞⎜⎜⎝

⎛

−Φ

−=Δ−−−

+−−

−−−

+−−

1

ˆ

1

ˆ1

ˆ

1

ˆ

1111

1111

. (4)

The expected change in the interest rate, denoted ∆it

e, is a function of the inverted cumulative distribution function Φ-1(⋅), and an error term εt. Inserting a proportion, P, into the function Φ-1(⋅) gives the corresponding standardized cumulative normal distribution value. The survey data provides us with the sample proportions for those who answer “Up”, denoted , and those who answer “Down”, denoted . The

parameters are set to α = 0.01 and δ = 1%.

+−1tP −

−1tP21 The value of α is based on the observation

that the “Don´t know”-fraction fluctuates between 0.01 and 0.05.22 To check the sensitivity of data to changes in α I calculated the expectations with different values of α. The difference between the estimates turned out to be small, with differences within a couple of basis points, which indicate that the choice of α is not critical. The choice of δ is rather arbitrary since it will only change the scaling of the average expected change. The chosen value implies that individuals with an absolute expected interest rate change below one percentage point will answer “Same” in the survey. This value seems plausible for a twelve month expectation of the interest rate change.

This survey measure is associated with some problems that we need to address. First of all, the survey question concerns what the respondents think will happen to “interest rates for borrowing money”, i.e. the bank lending rates. This is a much broader definition of interest rates than what the futures and VAR forecast measures refer to. The survey definition refers to market interest rates, rather than the FFRT which is controlled by the central bank. However, the market rates are related to the FFRT through the expectations hypothesis of the term structure, indicating that market rate expectations can be used as a proxy for FFRT expectations. There is also a strong statistical relation between lending rates and the target rate, with the correlation

20 For different derivations of this formula see Carlson and Parkin (1975), and Nolte and Pohlmeier (2004). 21 Note that α is a fraction, and δ is expressed in the same units as the underlying variable, ∆it

e. 22 With α constant it cannot be allowed to be larger than 0.01 since 0 ≤ α ≤ Dt, with Dt being the “Don´t Know”-fraction of the answers. This value is also supported by an OLS estimate of α that I made, which is one of the estimation methods that Carlson and Parkin (1975) suggests. This estimate indicates α = 0.01089.

22_____________________________________________________________________________________Measuring Expectations

coefficient between the prime lending rate and the FFRT at 0.998 for monthly observations.

The second issue concerns the fact that the survey question refers to the expected development “during the next twelve months”, while the other measures of expectations in this paper has a horizon shorter than one month. This implies that the survey is measuring expectations over a longer horizon than the other methods. It also generates overlapping data since we have monthly observations of twelve month expectations. To obtain comparable expectations I divide the estimated change in the FFRT by eight, based on a naive but straightforward assumption about having the twelve month change executed by the Fed in equal steps at the eight different FOMC meetings during the upcoming twelve months. It can be argued that the expectations over a twelve months horizon should be front-loaded, i.e. that a larger part of the expected twelve month change is expected to be implemented during the first month(s) than towards the end of the period. In practice, the appropriate factor for scaling the twelve month expectations is between eight and one. However, this scaling factor is irrelevant for the qualitative results of the investigation as it does not affect the correlations between the measures.23

3 Data

The FOMC has eight scheduled meetings per year, approximately every six weeks, where any changes to the FFRT are decided and announced. The sample period covers target rate decisions made by the FOMC between February 1994 and December 2004. Pre-1994 data are excluded because there is a distinctive change in the Fed announcement policy, starting the 4th of February 1994. From this day the FOMC meetings have been followed by an official statement disclosing the decision about the target rate. Pre-1994 there were no such official announcements and the changes in FFRT were not easy to pinpoint in time.24

The purpose of the study is to investigate how the expectations measures function during normal conditions. Therefore, I have excluded the five meetings during the sample period that were not scheduled ahead, since unscheduled meetings occur during crises or major unexpected events. I also exclude the observation of the 31st of January

23 The quantitative results for the slope coefficient of the bias test and the descriptive statistics will be affected since the scale factor changes the magnitude of the expected change. However, the point estimates of the correlation coefficients are not affected at all by changes in the scale factor. 24 Söderström (2001) also argues that the trading volume in the federal funds rate futures was fairly low before 1994, which could imply more noisy price quotes for these futures contracts due to for instance large bid-ask spreads.

_____________________________________________________________________________________23

2001, since this was a scheduled meeting that took place shortly after the unannounced meeting at the 3rd of January 2001 and the futures method is not valid with two meetings in the same month.25 This leaves me with 87 observations for the sample period.

The Federal funds rate, the Federal funds rate futures prices and the Goldman & Sachs Commodity Index have been retrieved from Hansson & Partners AB. The real-time variables used in the CEE-VAR are collected from the website of Federal Reserve Bank of Philadelphia.26 The Michigan Consumer survey data are publicly available at the website of University of Michigan.27 More information on data sources is available in the appendix.

4 Comparing the Measures of Expectations

The different methods to measure expectations are here compared to each other, to reveal differences and similarities. Since the three methods of measuring expectations are fundamentally different I expect the measurement errors from these methods to have low correlation between them. This implies that similarities between the measures indicate that the measures are picking up the same unobserved phenomenon, i.e. the true expectations. I compare the descriptive statistics for the measures of expected changes, as well as for the unexpected changes. I also plot the expectations measures against each other and compute pairwise correlations.

4.1 Descriptive Statistics Comparison

The time series characteristics of expected changes are displayed in Figure 2a-d and in Table 1, while those of unexpected changes are found in Figure 3 and Table 2. The results from the tests of a forecast bias for the expected changes are shown in Table 3.

25 Excluding the observations mentioned above has no significant impact on the results. 26 http://www.phil.frb.org/econ/forecast/readow.html 27 http://www.sca.isr.umich.edu/

24_____________________________________________________________________________________Measuring Expectations

Figure 2 Expected Changes of FFRT

a) Estimates of Futures Method 1994-2004

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FUTURES EXPECTATIONS FFRT CHANGE

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b) Estimates of Survey Method 1994-2004

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The sample contains scheduled FOMC meetings from January 1994 to December 2004. FFRT CHANGE is the realized change of the Federal funds rate target. Each graph shows the expected changes in the FFRT for the scheduled FOMC meetings as estimated by a particular expectations measure. The numbers are in basis points. Gaps in the graphs are due to excluded observations.

_____________________________________________________________________________________25

c) Estimates of CEE-VAR Forecast Method 1994-2004

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CEE-VAR EXPECTATIONS FFRT CHANGE

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ints

d) Estimates of ALT-VAR Forecast Method 1994-2004

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ALT-VAR EXPECTATIONS FFRT CHANGE

Basi

s Po

ints

The sample contains scheduled FOMC meetings from January 1994 to December 2004. FFRT CHANGE is the realized change of the Federal funds rate target. Each graph shows the expected changes in the FFRT for the scheduled FOMC meetings as estimated by a particular expectations measure. The numbers are in basis points. Gaps in the graphs are due to excluded observations.

26_____________________________________________________________________________________Measuring Expectations

Figure 3 Unexpected Changes of FFRT 1994-2004

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FUTURESSURVEY

CEE-VARALT-VAR

Basi

s Po

ints

The sample contains scheduled FOMC meetings from January 1994 to December 2004. The graph shows the unexpected change in the FFRT for the FOMC meetings as estimated by the four different expectations measures. The numbers are in basis points. Gaps in the graph are due to excluded observations.

Table 1

Descriptive Statistics: Expected Changes of FFRT

Futures-

Expectation

Survey-

Expectation

CEE-VAR

Expectation

ALT-VAR

Expectation

Actual

Change

Mean 2.7727 16.3220 -3.3483 -2.7386 1.4368

Median 0.7045 14.9875 -5.6300 0.4100 0.0000

Maximum 50.7273 46.2313 67.0800 29.0300 75.0000

Minimum -68.2000 -9.0300 -157.2800 -100.3500 -50.0000

Std. Dev. 21.5170 11.8186 37.3578 18.1510 22.0189

Skewness -0.3447 0.2048 -0.9878 -2.6997 0.1965

Kurtosis 4.3070 2.7917 6.1225 14.0320 4.7509

Observations 77 87 87 87 87

The expected changes are expressed in basis points. The sample is from January 1994 to December 2004 and the observations are pre-scheduled FOMC-meetings.

_____________________________________________________________________________________27

Table 2

Descriptive Statistics: Unexpected Changes of FFRT

Futures Survey CEE-VAR ALT-VAR

Mean -1.1493 -14.8853 4.7851 4.1754

Median -0.5833 -14.9875 5.6300 2.3100

Maximum 68.2000 39.4713 120.5300 81.2700

Minimum -50.7273 -58.6688 -77.7400 -52.1300

Std. Dev. 15.5070 16.2995 40.3693 22.4984

Skewness 0.6243 0.2153 0.4682 0.6030

Kurtosis 8.4371 3.9353 3.5078 4.6764

RMSE 15.449 22.004 40.421 22.369

MAE (MAD) 9.723 18.339 30.509 16.374

Autocorrelation

Lag 1 -0.269** -0.181* 0.081 0.263**

Lag 2 0.225** 0.275** 0.084 0.350***

Lag 3 -0.246** -0.206* 0.194* 0.069

Lag 4 0.051 0.290*** 0.249** 0.228**

Q(9) 18.015** 23.052*** 11.698 26.724***

Observations 77 87 87 87

The unexpected changes are expressed in basis points. The sample is from January 1994 to December 2004 and the observations are pre-scheduled FOMC-meetings. RMSE is the root mean squared errors and MAE is the mean absolute error. */**/*** = indicates if a test is significantly different from zero at 10% / 5% / 1% significance level. The autocorrelation tests are individual tests for the first four lags and a joint Q-test for the n first lags.

Starting with the futures measure, we can see that the average unexpected change,

i.e. the average forecast error, is not even two basis points from zero. The variation of the forecast errors goes between +68 basis points and -51 basis points, and the standard deviation is about 16 basis points. The bulk of the forecast errors are centred close to zero but a few observations are large, which is reflected in a kurtosis value of 8.437. Thus forecast errors are typically rather small, i.e. the futures measure of expectations is

28_____________________________________________________________________________________Measuring Expectations

relatively successful in forecasting the true change in FFRT. The bias test regression in Table 3 confirms this observation. This test simply regress the true change in FFRT on the expected change, as measured by each measurement method:

[ ] ttt FFRTEFFRT εβα +Δ⋅+=Δ . (5)

A non-biased forecast gives a zero constant and a slope equal to one.28 The constant term for the futures measure is not significantly different from zero, and the slope term is not significantly different from one, indicating that this is indeed an unbiased measure. This becomes even more apparent when we look at the plot in Figure 4, where it is clearly shown that a positive (negative) expected change is typically followed by a positive (negative) change in FFRT, or possibly no change at all. The observations line up nicely around the 45-degree line, which is reflected in the high R2 of 0.565 for the bias test regression.

Table 3 Bias Test Regressions

Regressors Futures Survey CEE-VAR ALT-VAR

Intercept

(H0: α=0)

-0.59

(-0.3509)

-19.53

(-5.615)***

1.74

(0.543)

2.72

(0.908)

Slope

(H0: β=0)

(H0: β=1)

0.7969

(5.4979)***

(-1.4007)

1.2845

(7.991)***

(1.770)*

0.0898

(1.181)

(-11.969)***

0.4676

(5.117)***

(-5.826)***

R2 adjusted 0.565 0.469 0.012 0.139 The regression is: [ ] ttt FFRTEFFRT =α + β ⋅ Δ +εΔ

[ tFFRTE Δ ]

is the estimated expected change of the FFRT (federal funds rate target) in basis points. The values in parentheses are t-values. The standard errors are Newey & West adjusted. */**/*** = indicates if a double-sided t-test is significantly different from the H0-hypothesis at 10% / 5% / 1% significance level. The sample is from January 1994 to December 2004 and the observations are pre-scheduled FOMC-meetings.

28 Since the true change in FFRT is a discrete variable, moving in steps of 25 basis points, this OLS-based test may be inaccurate. To control for that possibility and its impact on the inference I conduct the same regression test using a monthly average of the related market traded FFR, which is not limited to the 25 basis point steps. Both types of tests yield the same qualitative results for the futures measure.

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Figure 4 FFRT Change vs. Futures Measure Expected Change

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50

100

150

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FUTURES EXPECTATIONS

FFR

T C

HA

NG

E

The sample contains scheduled FOMC meetings from January 1994 to December 2004. Each ring in the plot represents one of the FOMC meetings. FFRT CHANGE is the realized change of the Federal funds rate target. FUTURES EXPECTATIONS are the expected changes in the FFRT as estimated by the futures method. The numbers are in basis points.

The survey measure has an average unexpected change of -14.88 basis points,

which is large compared to the futures measure at -1.15. The highest and lowest errors are +39.47 and -58.67 and the standard deviation is 16.30 basis points, which is similar to the futures measure. As we can see in Figures 2b and 5, the survey measured expectations consistently indicate more positive changes than the realized true change in FFRT, which leads to many negative forecast errors. The average expected change is +16.32 basis points, again indicating that the agents in the economy very often believe in an increase of the target rate. The observation that survey expectations on average show positive expected changes in the FFRT is not dependent on the use of the Carlson and Parkin (1975) method, or the timing adjustment procedure. This characteristic can be observed in the raw data of the qualitative survey. Most of the time, the largest fraction of consumers are those who answer that interest rates will go up.29

29 A conceivable explanation for this observation is that since the survey has a twelve month expectations horizon it can pick up expected changes in the FFRT beyond the next FOMC meeting. The spread between the one-year US government bond and the FFR has a mean of +16 basis points over the sample

30_____________________________________________________________________________________Measuring Expectations

Figure 5

FFRT Change vs. Survey Measure Expected Change

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SURVEY EXPECTATIONS

FFR

T C

HA

NG

E

The sample contains scheduled FOMC meetings from January 1994 to December 2004. Each ring in the plot represents one of the FOMC meetings. FFRT CHANGE is the realized change of the Federal funds rate target. SURVEY EXPECTATIONS are the expected changes in the FFRT as estimated by the survey method. The numbers are in basis points.

The bias is also detected in the bias regression test for the survey measure, as the

constant term is -19.53 basis points and significantly different from zero.30 The estimated slope of this regression is a function of how the twelve month survey expectations are scaled down. With a downscaling factor of 8, the point estimate of the slope is 1.285 which is significantly different from unity at the ten percent significance level, but not at five percent.31 The regression R2 is 0.469, which is slightly lower than what we observed for the futures measure. The feature of the survey measure that stands period, which is significantly positive at the one percent significance level. The median value is eleven basis points. According to the Rational expectations hypothesis of the term structure a positive spread indicates that the market expects increases in the short-term interest rates. The difference between the survey measure horizon and the time to the next FOMC meeting could therefore cause the constant bias we observe for the survey measure in Table 3. 30 Since the survey expectations have an overlapping problem I use an 11-lag Newey & West covariance matrix for the survey bias test. The other tests have a Newey & West covariance matrix with 3 lags to counter possible serial correlation. 31 The bias test using the FFR instead of the FFRT gives a slope point estimate that is significantly different from one at the 1% level.

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out in Table 3 is the constant positive bias, confirmed by both the plot and the statistical estimates.

The CEE-VAR measure has a fairly small average forecast error, only +4.79 basis points compared to -14.88 for the survey measure. However, the bias test in Table 3 and the plot in Figure 6 show that the CEE-VAR measure of expectations is a poor forecasting tool. The slope coefficient of the bias test regression is not significantly different from zero and the R2 is only 0.012. The span of the forecast errors go from -77.74 to +120.53 basis points, and the standard deviation is 40.37 basis points. This variation in the forecast errors is much higher compared to the survey and futures measures, which have standard errors of around only 16 basis points. The CEE-VAR expected change series also display large variation, with rather large expected changes and little resemblance with the realized change of the FFRT. The poor forecasting ability of the CEE-VAR has been noted in previous studies (Evans & Kuttner, 1998). By themselves, the results for the CEE-VAR method do not imply that this is a poor expectations measure, but when compared to the other two measures it seems unlikely that the CEE-VAR measure reflects the true expectations. The agents of the economy would have to be rather irrational to stick with expectations like those measured by the CEE-VAR method, showing such poor forecasting properties.

32_____________________________________________________________________________________Measuring Expectations

Figure 6 FFRT Change vs. CEE-VAR Measure Expected Change

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The sample contains scheduled FOMC meetings from January 1994 to December 2004. Each ring in the plot represents one of the FOMC meetings. FFRT CHANGE is the realized change of the Federal funds rate target. CEE-VAR EXPECTATIONS are the expected changes in the FFRT as estimated by the VAR forecast method, with the Christiano, Eichenbaum and Evans (1996) VAR specification. The numbers are in basis points.

The ALT-VAR, the simple 3-lag VAR in first differences, has similar averages

but a 22.50 basis points standard deviation of the forecast error, which is considerably lower than the standard deviation of the standard CEE specification. The bias test regression in Table 3 and the plot in Figure 7 present somewhat different results for the ALT-VAR compared to the standard CEE-VAR. The slope is now significantly different from zero, which was not the case for the CEE-VAR, but is still significantly different from one. R2 is much higher than for the CEE specification, 0.139 compared to 0.012, but still not very impressive compared to the R2 of the non-statistical measures, which are around 0.500.32

32 Certainly we can find a particular VAR specification that is better at forecasting the FFRT during the time period of interest, but for an expectations measure we want a more robust and time invariant method that is not dependent on a very unique specification.

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Figure 7 FFRT Change vs. ALT-VAR Measure Expected Change

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The sample contains scheduled FOMC meetings from January 1994 to December 2004. Each ring in the plot represents one of the FOMC meetings. FFRT CHANGE is the realized change of the Federal funds rate target. ALT-VAR EXPECTATIONS are the expected changes in the FFRT as estimated by the VAR forecast method, with a three-lag, seven-variable VAR specification in first differences. The numbers are in basis points.

Both VAR measures are subject to the timing issue discussed in the method

description. To control for the timing issue I exclude the FOMC meeting observations that take place during the first half of the month. The observations during the last half of a month would definitely have the full information set, i.e. all seven variables in VAR are publicly available. For the benchmark CEE-VAR there is no important difference between using all FOMC meetings and using only the FOMC meetings taking place during the last half of the month. The ALT-VAR specification seems to loose some of the forecasting ability when the sample is restricted. This indicates that the treatment of the timing issue could incorrectly improve the VAR measures; the forecasting ability of a VAR should then be even worse than what we see in Table 1 to 3.

34_____________________________________________________________________________________Measuring Expectations

4.2 Autocorrelations

Another characteristic of expectations that is appropriate to study is the autocorrelation structure of the unexpected changes. The autocorrelation of the estimated unexpected changes is interesting from a rationality point of view. Rational expectations implies no serial correlation since all available information, including previous expectation errors, should be included in the information set of the agents forming expectations.33

The unexpected changes from the futures method show significant autocorrelation coefficients for the first three lags, as shown in Table 2. The autocorrelation is negative for lag one and three, while lag number two is positive. A Q-test for the nine first lags rejects the null hypothesis of no serial correlation at the five percent significance level.

Since the survey measure has overlapping expectations horizons the estimated unexpected changes will have positive serial correlation if the expectations for the next twelve months do not change between surveys. However, this strong positive serial correlation cannot be seen in the sample autocorrelation coefficients. In fact, the survey measure has an autocorrelation pattern similar to the futures measure, with lag one and three being negative and only lag two being positive. However, the significance level for the negative coefficients is only at ten percent. Another difference compared to the futures measure is that the fourth lag for the survey measure is positive and significant at the one percent level, while the futures measure showed no indication of autocorrelation for this lag. The joint test of autocorrelation for the nine first lags is significant for the survey measure of unexpected changes.

The CEE-VAR specification does not show any obvious signs of autocorrelation.34 The Q-test can not reject the null hypothesis of no serial correlation. The ALT-VAR specification shows significant signs of serial correlation, with the Q-test rejecting the null hypothesis at the 1% level. Lag one and two are individually significant at the five percent and ten percent level respectively. Both specifications show an individual significant autocorrelation for lag four at the five percent level. The patterns of sample autocorrelation coefficients for the two VAR specifications do not resemble the patterns we observe for the futures and survey measure.

33 Rational expectations can result in positive autocorrelation if we have a small sample where there are extended periods of rationally expected changes that are not realized. For instance, expecting a very small probability of an extreme outcome could lead to repeated rational expectation errors that are showing autocorrelation. This is often referred to as the Peso problem for exchange rate expectations. 34 Note that this is not by construction since the VAR estimates of unexpected changes are out of sample forecasts.

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4.3 Correlations between Measures

The most interesting analytical tools when comparing measures of expectations are the calculation of correlations coefficients and the pairwise plots. By plotting the different measures of expected change in FFRT against each other we can observe to what extent the measures appear to capture the same phenomenon. If two measures measure the same thing, ignoring measurement errors, we would expect the observations to line up around the 45- degree line in the scatter plots. We would also expect a high correlation coefficient when there is a linear relation between the two measures.

In the plots of the benchmark CEE-VAR measure against the other two measures, Figure 8 and 9, there seems to be no obvious relation between the standard CEE-VAR measure and the other measures. This implies that the CEE-VAR measure gives a different estimate of the true expectations than the futures and survey measures do. The sample correlation coefficients between all measures are presented in Table 4. The sample correlation coefficient between CEE-VAR and the futures measure is only 0.149. The correlation between the CEE-VAR and the survey measure is not much higher: 0.152.35

Table 4

Correlation Coefficients – Expected Changes of FFRT

Futures Expectations

Survey Expectations

CEE-VAR Expectations

ALT-VAR Expectations

Futures Expectations 1 0.811 0.149 0.348

Survey Expectations 1 0.152 0.379

CEE-VAR Expectations 1 0.371

ALT-VAR Expectations 1

The sample is from January 1994 to December 2004 and the observations are pre-scheduled FOMC-meetings.

35 When I include the unannounced meetings in the data set, these correlation coefficients are even lower.

36_____________________________________________________________________________________Measuring Expectations

Figure 8 Futures Expectations vs. CEE-VAR Expectations

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The sample contains scheduled FOMC meetings from January 1994 to December 2004. Each ring in the plot represents one of the FOMC meetings. FUTURES EXPECTATIONS are the expected changes in the FFRT as estimated by the futures method. CEE-VAR EXPECTATIONS are the expected changes in the FFRT as estimated by the VAR forecast method, with the Christiano, Eichenbaum and Evans (1996) VAR specification. The numbers are in basis points.

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Figure 9 Survey Expectations vs. CEE-VAR Expectations

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The sample contains scheduled FOMC meetings from January 1994 to December 2004. Each ring in the plot represents one of the FOMC meetings. SURVEY EXPECTATIONS are the expected changes in the FFRT as estimated by the survey method. CEE-VAR EXPECTATIONS are the expected changes in the FFRT as estimated by the VAR forecast method, with the Christiano, Eichenbaum and Evans (1996) VAR specification. The numbers are in basis points.

In contrast to the CEE-VAR, the ALT-VAR measure seems to have some positive

correlation with the futures and survey measure. The correlation coefficients with the futures and the survey measure are considerably higher than for the CEE-VAR, 0.348 and 0.379 respectively. This relation can also be observed in the plots of Figure 10 and 11.

38_____________________________________________________________________________________Measuring Expectations

Figure 10 Futures Expectations vs. ALT-VAR Expectations

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The sample contains scheduled FOMC meetings from January 1994 to December 2004. Each ring in the plot represents one of the FOMC meetings. FUTURES EXPECTATIONS are the expected changes in the FFRT as estimated by the futures method. ALT-VAR EXPECTATIONS are the expected changes in the FFRT as estimated by the VAR forecast method, with a three-lag, seven-variable VAR specification in first differences. The numbers are in basis points.

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Figure 11 Survey Expectations vs. ALT-VAR Expectations

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The sample contains scheduled FOMC meetings from January 1994 to December 2004. Each ring in the plot represents one of the FOMC meetings. SURVEY EXPECTATIONS are the expected changes in the FFRT as estimated by the survey method. ALT-VAR EXPECTATIONS are the expected changes in the FFRT as estimated by the VAR forecast method, with a three-lag, seven-variable VAR specification in first differences. The numbers are in basis points.

As a more formal test of correlation I calculate the Spearman rank correlation

coefficients, shown in Table 5. This non-parametric measure shows a significant positive correlation between the futures measure and the ALT-VAR measure at the one percent significance level.36 The ALT-VAR measure and the survey measure show a significant positive correlation at the one percent level.37 The standard CEE-VAR shows no significant correlation with any of the other two measurement methods. Evans and Kuttner (1998) find a similar pattern when they investigated the correlation between forecast errors from the CEE-VAR and unexpected changes in FFRT measured with a futures method similar to the one used in this paper. They conclude that forecast errors

36 The advantage of using a Spearman rank correlation coefficient test is that no assumption about joint normality is needed. The test is a one-sided test for a positive correlation coefficient. 37 The inference for ALT-VAR correlations are changed when I control for the timing issue by excluding the FOMC meetings taking place in the first half of the month. The correlation coefficient with the survey measure is not significant, and correlation between ALT-VAR and the futures measure is only significant at the ten percent level.

40_____________________________________________________________________________________Measuring Expectations

from a VAR with fewer lags are more closely related to the forecast errors of a futures method than the standard twelve lag CEE-VAR. I show similar results, but for correlations between expected changes instead of unexpected changes.

Table 5

Spearman Rank Correlation Coefficient Test – Expected Changes

Futures Expectations

Survey Expectations

CEE-VAR Expectations

ALT-VAR Expectations

Futures Expectations 1 0.818*** 0.074 0.287***

Survey Expectations 1 0.114 0.292***

CEE-VAR Expectations 1 0.522***

ALT-VAR Expectations 1

The Spearman rank correlation coefficient test use a t-test procedure with a zero correlation null hypothesis. */**/*** = indicates if the point estimate is significantly different from zero at 10% / 5% / 1% significance level (single-sided test for positive correlation). The sample is from January 1994 to December 2004 and the observations are pre-scheduled FOMC-meetings.

The comparison of the futures measure versus the survey measure, plotted in

Figure 12, reveals some interesting results. The plot displays what appears to be a linear relation between these two measures, but with a negative intercept. The slope of this linear relation is not one, but it is very much affected by the ad hoc time horizon adjustment of the survey measure. For instance, if the survey time horizon adjustment is set to be one fourth, instead of one eighth, of the full year survey expectation, we get a relation which is close to one for one, as we can see in Figure 13.38

38 This type of adjustment could be justified by a “myopic agents”-argument where imminent events get a higher weight than more distant events.

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Figure 12 Futures Expectations vs. Survey Expectations

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The sample contains scheduled FOMC meetings from January 1994 to December 2004. Each ring in the plot represents one of the FOMC meetings. FUTURES EXPECTATIONS are the expected changes in the FFRT as estimated by the futures method. SURVEY EXPECTATIONS are the expected changes in the FFRT as estimated by the survey method. The numbers are in basis points.

42_____________________________________________________________________________________Measuring Expectations

Figure 13 Futures Expectations vs. Survey Expectations II

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The sample contains scheduled FOMC meetings from January 1994 to December 2004. Each ring in the plot represents one of the FOMC meetings. FUTURES EXPECTATIONS are the expected changes in the FFRT as estimated by the futures method. SURVEY EXPECTATIONS II are the expected changes in the FFRT as estimated by the survey method, but with a more front-loaded adjustment of the original twelve-month expectation than the estimate from Table 12 (one fourth instead of one eighth). The numbers are in basis points.

The correlation coefficient between the futures and the survey measure is 0.811

and indicates a strong linear relationship.39 The Spearman rank correlation coefficient test indicates that there is a positive and significant correlation between these two measures at the one percent significance level. This high correlation is robust to including the five unannounced meetings during the sample period.40 Hence, these two measures appear to capture the same underlying phenomenon. The most likely explanation is that they both measure the true expectations. A high correlation coefficient could be caused by a high correlation between the measurement errors from these two measures, without any of the measures picking up the true expectations.

39 Note that the correlation coefficient is not affected by how we scale the survey expectations. 40 It is also robust to excluding FOMC meetings in the first half of the month, with the correlation coefficient still above 0.75.

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However, since the measures are fundamentally different in their construction I claim that such high correlation between their measurement errors is not likely.

These two measures of expectations are statistically related, but with a constant shift where the survey expectations are tilted towards positive changes in the FFRT. This bias towards positive changes in the survey measure of expectations was revealed already in the descriptive statistics and the bias test regression.41

The focus of the preceding analysis is on the correlation between the different measures of estimated expected change. However, a comparison of different measures can also be done by analyzing the correlation between the estimates of unexpected changes, even though this approach has a drawback. As, Evans and Kuttner (1998) pointed out, the correlation between unexpected changes is a misleading indicator since it includes different covariances between the true change in FFRT and the two different expectations measures.42 To compare the two approaches of correlation measurement, and to make the analysis complete, Table 6 reports the correlation coefficients between the unexpected changes suggested by each measure. The correlation coefficient between the futures method and the survey method is 0.626, which is lower than the correlation coefficient between the survey measure and the ALT-VAR measure, 0.655. Otherwise, the pattern of correlations between unexpected changes is similar to the correlation pattern of expected changes, but the differences between the coefficients are less pronounced.

41 I also find that the spread between the one-year US government bond and the FFR is correlated with both the survey and the futures measure, with correlation coefficients 0.746 and 0.767. These high correlations are not surprising since the spread is linked to interest rate expectations through the Rational expectations hypothesis of the term structure. When I orthogonalize both the survey and the futures measure to the spread, the correlation between these two measures is still significant with a correlation coefficient of 0.529. 42 For instance, Evans and Kuttner (1998) showed that the forecast errors from a naive “no change” forecast had a high correlation with the forecast errors of a futures model forecast. These two forecast models give extremely different forecasts, and yet the correlation coefficient between the forecast errors is high, showing the weakness of using this kind of correlation to determine similarities between different expectations measures.

44_____________________________________________________________________________________Measuring Expectations

Table 6 Correlation Coefficients – Unexpected Changes of FFRT

Futures Expectations

Survey Expectations

CEE-VAR Expectations

ALT-VAR Expectations

Futures Expectations 1 0.626 0.186 0.334

Survey Expectations 1 0.375 0.634

CEE-VAR Expectations 1 0.503

ALT-VAR Expectations 1

The sample is from January 1994 to December 2004 and the observations are pre-scheduled FOMC-meetings.

5 Conclusions

How can we evaluate the validity of the available measures of expectations when the variable to be measured, the true expectations, is not observable? This paper proposes a solution to the problem by comparing fundamentally different methods of measuring expectations. A comparison of measures will detect similarities and differences, and this helps us to evaluate whether the methods do measure the true expectations. This procedure is applied to the expectations on the target interest rate of the Fed, the FFRT, which is an appropriate variable since there are several methods available to measure expectations: VAR forecast measures, survey measures and futures market measures.

The results show that the VAR forecast method can result in quite different expectations depending on what specification one use. The VAR forecast measures all show inferior forecasting abilities compared to the survey and the futures measures. This could indicate that agents use more information than just the variables included in the VAR. In particular it turns out that a VAR in first differences and with few lags has both smaller variations in the forecast errors, and higher correlations with the other two methods in this study, compared to the benchmark twelve lag VAR in levels proposed by Christiano, Eichenbaum and Evans (1996). The survey method indicates expectations with a significant constant bias. The survey respondents often claim to expect positive changes to the Fed target rate and on average they overestimate the FOMC decision on the change of the target rate. The measured expectations from the

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futures method have no significant bias and relatively small forecast errors. Despite this difference in forecasting ability, the survey method and futures method produce expectations that are highly correlated. The correlation coefficient for these two measures of the expected change in the target rate is 0.81. Another similarity between the futures measure and the survey measure is observed in the patterns of sample autocorrelations for estimated unexpected changes. Both measures have significantly negative autocorrelation for the first and third lag and positive for the second lag, which means both measures show the same pattern of irrationality in the expectations.

The implied market expectations derived from the Federal funds futures and the transformed responses from the Michigan consumer survey are fundamentally different methods to measure expectations. This makes it highly unlikely that the underlying relation between them is due to correlated measurement errors. I have not found any other likely explanation for this high correlation than the presumption that they both capture the true expectations.

The survey measure reflects the expectations of consumers, while the futures measure corresponds to market expectations. The true expectations of the consumers and of the futures market participants are not necessarily the same. Despite the possible difference between these two expectations measures the correlation is high. This indicates a remarkable coherence between the expectations of consumers and futures market participants.

These results can be further explored if we can obtain other survey data on interest rate expectations and refine the comparison method. By studying the measures of expectations for other variables we will be able to learn and understand more about the nature of the true expectations, and thereby improve our ability to construct useful theoretical economic models.

46_____________________________________________________________________________________Measuring Expectations

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Price Setting and the Long-Run Phillips Curve”, Brookings Papers on Economic Activity, 2000, p. 1-44.

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to Federal Reserve Policy?”, Journal of Finance 60 (3), June 2005, p. 1221-1257. Carlson, John A. and Michael Parkin, “Inflation Expectations”, Economica 42, 1975, p.

123-138. Christiano, Lawrence J., Martin Eichenbaum and Charles Evans, “The Effects of

Monetary Policy Shocks: Evidence from the Flow of Funds”, The Review of Economics and Statistics 78 (1), February 1996, p. 16-34.

Dasgupta, Susmita and Kajal Lahiri, “A Comparative Study of Alternative Methods of

Quantifying Qualitiative Survey Responses Using NAPM Data”, Journal of Business & Economic Statistics 10 (4), October 1992, p. 391-400.

Durham, J. Benson, “Estimates of the Term Premium on Near-dated Federal Funds

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Evans, Charles L. and Kenneth N. Kuttner, “Can VARs Describe Monetary Policy?”,

Working Paper SeriesWP-98-19, Federal Reserve Bank of Chicago, 1998. Faust, Jon, John H. Rogers, Eric Swanson and Jonathan H. Wright, “The high-

frequency response of exchange rates and interest rates to macroeconomic announcements”, Journal of the European Economic Association 1 (5), September 2003, p. 1031-1057.

Gürkaynak, Refet S., Brian Sack and Eric Swanson, “Market-Based Measures of

Monetary Policy Expectations”, Finance and Economics Discussion Series 2002-40, Board of Governors of the Federal Reserve System (U.S.), 2002.

Gürkaynak, Refet S., “Using Federal Funds Futures Contracts for Monetary Policy

Analysis”, Finance and Economics Discussion Series 2005-29, Board of Governors of the Federal Reserve System (U.S.), 2005.

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Gürkaynak, Refet S., and Justin Wolfers, “Macroeconomic Derivatives: An Initial

Analysis of Market-Based Macro Forecasts, Uncertainty and Risk”, Working Paper Series 2005-26, Federal Reserve Bank of San Francisco, 2005.

Johansson, Fredrik, “A Measurement Error Analysis of Survey Response Data”, in

Essays on Measurement Error and Nonresponse, Economic Studies 103, Department of Economics, Uppsala University, 2007, p. 13-46.

Krueger, Joel T. and Kenneth N. Kuttner, “The Fed funds futures rate as a predictor of

Federal Reserve policy”, Journal of Futures Markets 16 (8), December 1996, p. 865-879.

Kuttner, Kenneth N., “Monetary policy surprises and interest rates: Evidence from the

Fed funds futures market”, Journal of Monetary Economics 47 (3), June 2001, p. 523-544.

Lai, Kon S., “On Structural Shifts and Stationarity of the Ex Ante Real Interest Rate”,

International Review of Economics and Finance 13(2), 2004, p. 217-228. Mitchell, James, “The Use of Non-normal Distributions In Quantifying Qualitative

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Data Appendix Federal Funds Rate and Target Rate The monthly data for the FFR and FFRT were supplied by the Fed through Hanson & Partners AB.43 The FFR data are a monthly average over the daily rates, while the FFRT data consists of the prevailing target rate of the Fed at the last day of each month. In addition to the monthly data the Federal Reserve webpage provides the dates of the FOMC meetings as well as the exact changes in the target rate at each meeting.44 Additional information about the exact timing of the FOMC meetings is available in Kuttner (2001). Futures The Fed funds futures rate data were supplied by the Hanson & Partners AB. The futures contracts are traded at the Chicago Board of Trade (CBOT).45 The underlying asset for these futures contracts is a 30 day average of the effective FFR for a particular month. I use the close daily rate for the spot futures rate of the month of the FOMC meeting of interest, i.e. the futures contracts with the settlement date at the end of that month. I also use the last close daily rate observation of a one-month futures contract before it turns into the spot contract. Survey The Michigan Consumer survey data is supplied by the University of Michigan at their public website.46 The survey observations are made at a monthly interval and present the proportions of the answers that reply “Up”, “Down”, “Same” and “Do not know”. Note that the survey question of interest in this paper is only one of many survey questions that the respondents are asked.

43 See http://www.ecowin.com/ for the information webpage about the Ecowin database of Hanson & Partners AB. Note that Hanson & Partners AB was acquired by Reuters Ltd. in November 2005. 44 See for instance http://www.federalreserve.gov/FOMC/#calendars. 45 http://www.cbot.com/ 46 http://www.sca.isr.umich.edu/

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VAR Variables All VAR variables are on a monthly frequency. The real-time announcements of seasonality adjusted payroll employment (N), Consumer Price Index (CPI), non-borrowed reserves (NBR), total reserves (TR), and the monetary aggregate M1, were supplied by the Federal Reserve Bank of Philadelphia.47 The twelve month moving average of monthly growth rates of Goldman & Sachs Commodity Index (GSCI) was supplied by the Hanson & Partners AB. The monthly GSCI are monthly averages over the close daily return index.

47 http://www.phil.frb.org/econ/forecast/readow.html

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Essay 2

A Critical Look at Measures of Macroeconomic Uncertainty

1 Introduction

Uncertainty constitutes a crucial element in modern macroeconomic theories and

policy analyses. Since uncertainty cannot be directly observed, we must use proxies

in economic applications. It is therefore surprising that few studies have taken a

critical look at available proxies of macroeconomic uncertainty to discern which

are more appropriate as measures of uncertainty. In the few studies that exist,

some preferred proxy is usually assumed to be the correct measure of uncertainty,

and other proxies are evaluated by comparison with this preferred proxy. Such a

procedure requires that we know a correct measure of uncertainty, at least ex post,

which is something we really cannot know with any certainty.

In this paper, we offer an alternative narrative methodology that does not take

a stand, ex ante, on a preferred proxy. Instead, we subject all available proxies to

a test where we study if they react as expected to exogenous shocks to uncertainty.

Moreover, we argue that although different proxies of uncertainty are connected to

different macroeconomic variables, they should be positively correlated under rea-

sonable assumptions. We empirically investigate whether this is the case. Moreover,

given that uncertainty could vary substantially across different variables, we ask the

question whether different types of uncertainty share a common factor.

The most commonly used proxy of uncertainty in applied work is some proxy of

stock market volatility (e.g. Romer (1990) and Hassler (1996)). This proxy is usually

employed without due motivation or reference to why stock market volatility would

be appropriate. In this paper, we also consider uncertainty proxies derived from

surveys, targeted both at professional forecasters and the general public. These

proxies are disagreement proxies, as they reflect the disparity of individual point

forecasts. The ability of such disagreement proxies to capture aggregate uncertainty

has been discussed in some papers (Zarnowitz and Lambros (1987) and Giordani and

Söderlind (2003) inter alia). The general conclusion seems to be that disagreement

proxies have reasonable properties as measures of uncertainty, and they have been

extensively used; see e.g. Bomberger (1996) and Sepulveda (2003) who also provide

further references. Finally, we also consider probability forecast proxies obtained

from professional forecasters who assign probabilities to interval outcomes of key

variables. From a theoretical point of view, this type of proxy is appealing since

an approximation of the entire probability distribution is used to construct the

uncertainty proxy.

We also try to evaluate the effects of uncertainty on aggregate consumption and

residential investment. This can provide some further evidence on the usefulness

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of available proxies. We also study the co-movement of various uncertainty proxies

with the business cycle.

The results can be summarized as follows. The (implied) volatility proxy be-

haves as expected since it increases for exogenous events such as terrorist attacks

and outbreaks of war, and decreases at presidential election outcome dates. The

disagreement proxies also increase in response to events of conflict and financial cri-

sis. Surprisingly, the probability forecast proxies do not react in any systematic way

to these events. This finding is of special importance since the probability forecast

proxies have been posited as "true" uncertainty and used to evaluate other proxies

(e.g. in Zarnowitz and Lambros (1987)). Such a supposition is dubious in the light

of our results. The correlation table of all available proxies indicates that most of

the various disagreement proxies are positively correlated. Furthermore, there are

some indications that volatility and probability forecast proxies are co-moving. Us-

ing factor analysis, we find only one common factor across different variable proxies

of uncertainty. This could be interpreted as there only being one fundamental factor

of uncertainty that shows up in most proxies. When we use proxies of uncertainty

in standard macroeconomic applications where uncertainty is supposed to be of im-

portance, we find all but the probability forecast proxies to be of importance. This

could be interpreted as further evidence of the inability of the probability forecast

proxies to pick up uncertainty. Finally, we look at the evolution of proxies in relation

to the business cycle. We find that uncertainty seems to be higher the further we

are from the normal level of real activity in the economy.

The paper is organized as follows. In section 2 we introduce the concept of un-

certainty within a simple model. The model is used to derive some properties of

uncertainty which are considered in the subsequent analysis. Section 3 describes

the different proxies considered. Section 4 attempts to evaluate uncertainty proxies

based on some narrative evidence. Section 5 uses factor analysis to extract common

factors across different proxies and Section 6 includes proxies of uncertainty in stan-

dard macroeconomic applications and examines how uncertainty co-moves with the

business cycle. Section 7 concludes.

54_____________________________________________________________________________________A Critical Look at Measures of Macroeconomic Uncertainty

2 A model motivation

The aim of this section is to give some structure to the way we think about macro-

economic uncertainty. We will discuss under what circumstances different types of

uncertainty are related. A simpleVAR model will be presented to illustrate how

uncertainty in different variables will co-move under reasonable assumptions. For

each variable, uncertainty is defined as its expected variance.

Consider a model economy that can be described by a trivariate VAR in GDP

growth (y), inflation (π) and interest rates (i). The first equation is an aggregate

demand relation; the second can be said to represent supply and the third describes

monetary policy. This model can be compactly written in matrix form as

AXt+1 = C +B(L)Xt + εt+1, (1)

with Xt =hyt πt it

i0, εt =

hε1,t ε2,t ε3,t

i0. εt is interpreted as the vector of

structural, unobserved, shocks to the economy.

Further, make the standard assumption that

Covt (εt+1) = Et

³εt+1ε

0t+1

´=

⎡⎢⎣ σ21,t+1 0 0

0 σ22,t+1 0

0 0 σ23,t+1

⎤⎥⎦ , (2)

indicating that the structural shocks are orthogonal to each other and have condi-

tional expected variances σ2t+1 =hσ21,t+1 σ22,t+1 σ23,t+1

i0. Note that we allow for

structural variances to be time-variant. Rewrite equation (1) in its reduced form by

pre-multiplying by A−1. We then get

A−1AXt+1 = A−1C +A−1B(L)Xt +A−1εt+1

Xt+1 = D +G (L)Xt + et+1 (3)

where et+1 are the reduced form residuals obtained by estimation. These observed

residuals are linear combinations of the structural shocks εt+1. Redefine A−1 = F

and write the residuals explicitly as

et+1 = Fεt+1. (4)

The coefficients in F capture the structural contemporaneous relations between the

variables in the VAR and the structural shocks. In general, all elements of F will

be non-zero so that the variance covariance matrix of the reduced form residuals

_____________________________________________________________________________________55

Ωt+1 6= 0 for all elements. The general expression for Ωt+1 becomes

Ωt+1 = Et

³et+1e

0t+1

´= Et

³Fεt+1ε

0t+1F

0´. (5)

The variances of the variables, the diagonal elements in Ωt+1, can be expanded as

V art(yt+1) = f211σ21,t+1 + f212σ

22,t+1 + f213σ

23,t+1, (6)

V art(πt+1) = f221σ21,t+1 + f222σ

22,t+1 + f223σ

23,t+1, (7)

V art(it+1) = f231σ21,t+1 + f232σ

22,t+1 + f233σ

23,t+1, (8)

where we see that the variance of each variable is a linear combination of all struc-

tural shock variances, σ2t+1. This implies that an increase in any element of σ2t+1 will

increase uncertainty of all variables. This occurs because of the contemporaneous

relations through the F -matrix.

Proposition 1 All proxies of uncertainty are expected to move in the same directionin response to any large exogenous shock of structural uncertainty.

Proposition 1 forms the basis for the narrative approach in section 4.1 where

we evaluate available proxies of uncertainty by examining how they react to events

which a priori should be expected to increase or decrease uncertainty.

In order to make statements about the possible correlations between V art(yt+1),

V art(πt+1), and V art(it+1), we need to consider the correlations of σ2t+1. According

to expressions (6)-(8), with positive correlations between the elements of σ2t+1, the

variances V art(yt+1), V art(πt+1), and V art(it+1) will also be positively correlated.

In fact, even if the elements of σ2t+1 are uncorrelated, we will still have positive

correlations among V art(yt+1), V art(πt+1), and V art(it+1) provided that the off-

diagonal elements in F differ from zero. Imagine that uncertainty about the demand

shock, σ21,t+1, suddenly increases and σ22,t+1 and σ23,t+1 are unchanged. Since all

expected variable variances contain σ21,t+1, the correlations between the variances

should be positive.1 2 This result is summarized in a second proposition.

Proposition 2 If structural shock variances, σ2t+1, are non-negatively correlatedand at least one structural shock has contemporaneous effects on all variables in the

economy, uncertainty about all variables will be positively correlated.

1However, the correlations might be very small, but nevertheless positive. The size of therelation depends on the coefficients in F and the relative size of structural shock variances.

2Alternatively, if we assume the Choleski decomposition with f12 = f13 = f23 = 0, as iscommonly done in the monetary policy literature, then all variables will share the σ22,t+1 componentand there will still be positive correlation.

56_____________________________________________________________________________________A Critical Look at Measures of Macroeconomic Uncertainty

This proposition indicates that the expected variance of any relevant macro-

economic variable should in theory reflect a conception of general macroeconomic

uncertainty, as it includes several or all elements of σ2t+1. In section 4.2, we study the

correlation table of all available proxies to see whether this expected result holds.

The model suggests that we could have as many underlying factors of uncer-

tainty as the number of variables. But it may be the case that, e.g., σ21,t+1 varies

where σ22,t+1 and σ23,t+1 are relatively stable. To investigate how many factors that

drive uncertainty, we will perform a factor analysis on the expected macroeconomic

variable variances in section 5.

3 Uncertainty proxies

Both expected levels and expected distributions are unobservable in the sense that

they are only available in the minds of the agents of the economy. While we can

usually observe the outcome of a variable to evaluate expected levels, the expected

distributions (i.e. uncertainty) have the disadvantage that there is no ex post ob-

servation of the actual conditional distribution. We exclude more complex methods

of estimating the whole expected distribution, and focus on easily interpreted prox-

ies of uncertainty that can be expressed by a single number, i.e. their expected

variances.3

The data are in monthly or quarterly frequency for the US from 1980 to 2005. For

several proxies, we cannot find data as far back as 1980, which means that we must

settle for what can be obtained. The proxies connected to the financial markets,

i.e. the volatility proxies, are available for higher frequencies but for comparison

purposes, we also use the monthly and quarterly versions of these proxies as well.

The acronyms are constructed according to the following logic. The first let-

ter of the acronym denotes the type of proxy method: "D" for disagreement, "P"

for probability forecast, and "V" for volatility. For the disagreement proxies we

have two additional subgroups, proxies belonging to the quantitative Survey of Pro-

fessional Forecasters and proxies belonging to the qualitative Michigan Consumer

Survey. Thus, after "D", the next letter denotes the subgroup: "S" for the Survey

of Professional Forecasters and "M" for the Michigan Consumer Survey. The last

letter for all acronyms denotes the variable connected to each specific proxy. Ta-

ble 1 illustrates the logic of the acronym constructions. See Tables 2 and 3 for a

description of data and data handling.

3The interested reader can consult Aguilar and Hördahl (1999) for a description on how toderive the full distribution of expectations through option pricing.

_____________________________________________________________________________________57

Table 1: Construction of acronyms for uncertainty proxiesFirst letter Second letter Third letterD (Disagreement) S (Survey of Prof. Forecasters) 7 variables, see Table 3

M (Michigan Consumer Survey) 8 variables, see Table 2V (Volatility) O (Implied, based on Option prices) See Table 2

H (Historical) See Table 2P (Probability forecast) Y (Real GDP % change) See Table 3

I (Inflation) See Table 3

Table 2: Acronyms and descriptions of uncertainty proxies

Acronym Description SampleDMB Business conditions during coming 12 months 1980m1-2005m6DMF Financial situation in 12 months 1980m1-2005m6DMH Buying conditions for houses 1980m1-2005m6DMR Expected change in interest rates the coming 12 months 1980m1-2005m6DML Buying conditions for large goods 1980m1-2005m6DMD Expected change in real family income the next years 1980m1-2005m6DMU Expected change in unemployment the coming 12 months 1980m1-2005m6DMV Buying conditions for vehicles 1980m1-2005m6VH Historical volatility, rolling 1-year standard deviation 1980m1-2005m12VO Implied volatility, monthly averages on daily OEX index 1986m1-2005m12

Note: Proxies derived from the Michigan Consumer Survey and Volatilities, monthly data

3.1 Stock market volatility proxies

A commonly used proxy for uncertainty is stock market volatility, which describes

the variability of stock market returns. The typical volatility proxy for a stock

market is the standard deviation, or variance, of stock index returns. Stock market

volatility is an example of a market based proxy of uncertainty.

We use two different stock market volatilities, historical (VH) and implied volatil-

ities (VO). The historical volatility is a moving standard deviation for a certain time

span. In this paper, we have included the monthly and quarterly frequencies for his-

torical volatility of the S&P 500 index during the last 12 months, based on daily

index returns. We have also included the implied stock market volatility, derived

from prices of stock index options, in the form of an implied volatility index known

as the VIX.4 Implied volatility can therefore be considered to be a more forward

looking proxy than historical volatility.

4Supplied by the Chicago Board Options Exchange (CBOE)

58_____________________________________________________________________________________A Critical Look at Measures of Macroeconomic Uncertainty

Table 3: Acronyms and descriptions of uncertainty proxies, cont’d

Acronym Description SampleDSP Expected %-change in corporate profits 4 quarters ahead 1980q1-2005q4DSI Expected CPI-inflation 4 quarters ahead 1981q3-2005q4DSH Expected %-change in new housing starts 4 quarters ahead 1980q1-2005q4DSC Expected %-change in real consumption 4 quarters ahead 1981q3-2005q4DSY Expected %-change in real GDP 4 quarters ahead 1981q3-2005q4DSR Expected T-Bill interest rate 4 quarters ahead 1981q3-2005q4DSU Expected unemployment rate 4 quarters ahead 1980q1-2005q4PY Probability distribution for changes in real GDP next year, sa 1992q1-2005q4PI Probability distribution for inflation next year, sa 1992q1-2005q4

Note: Proxies derived from the Survey of Professional Forecasters, quarterly data

3.2 Disagreement proxies

Another type of proxy for uncertainty is the disagreement proxy as derived from sur-

vey responses. This proxy typically observes the cross-sectional standard deviation

across individual point forecasts. It is important to recognize that this is a sim-

ple proxy of uncertainty as it only reflects the average disparity of the individuals’

expected means of the distribution.

The disagreement proxies are of two different types. The first type consists

of disagreement estimates based on quantitative point forecasts. These proxies all

come from the Survey of Professional Forecasters and include disagreement about

inflation (DSI), corporate profits (DSP), housing starts (DSH), real GDP (DSY),

real consumption (DSC), T-bill rate (DSR), and the unemployment rate (DSU).

The second type of disagreement proxies is based on qualitative survey data. The

data are presented as proportions of respondents who believe that a variable will go

up, down, or stay the same.5 To derive proxies of uncertainty we follow Lyhagen

(2001). By letting the proportions be parameters in a multinomial distribution,

we can calculate a variance to serve as a proxy of uncertainty. Let Pu denote

the proportion of respondents who answer "Up", and Pd denote those who answer

"Down". The sum of variances of these proportions becomes (1−Pu)Pu+(1−Pd)Pd.

This variance proxy imply that if one of these proportions is equal to unity, there is

no uncertainty, and if both proportions equal 0.5, uncertainty is at its maximum.

The qualitative proxies of disagreement used in this paper are all derived from

the Michigan Consumer Survey and include disagreement about business conditions

(DMB), financial situation (DMF), buying conditions for houses (DMH), borrowing

rate (DMR), buying conditions for large goods (DML), real family income (DMD),

5Or equivalently: "better", "same" or "worse".

_____________________________________________________________________________________59

unemployment rate (DMU), and buying conditions for vehicles (DMV).

3.3 Probability forecast proxies

The theoretically most appealing type of uncertainty proxy in this paper is what

Sepulveda (2003) refers to as the probability forecast proxy. It is appealing because

not only does it take into account disagreement but also the average individual

forecast distribution. The Survey of Professional Forecasters includes a section in

its questionnaire where the respondents are asked to state their expected probability

over intervals of GDP growth and inflation for the next year. This yields a histogram

representation of each forecaster’s expected distribution at a certain point in time,

making it possible to derive an average distribution of expectations.

In deriving the probability forecast proxies, we follow Sepulveda (2003) as we

first calculate each forecaster’s mean and standard deviation of the expectations at

t. Then, we simply take the average of the mean and the standard deviation, across

all forecasters, to obtain both the average mean and the average standard deviation.

Our derivation is somewhat different from what is used in Sepulveda (2003), as

we acknowledge the seasonality in the series and use a seasonal dummy approach to

adjust for this pattern. The reason for seasonality is the declining forecast horizon as

the forecaster approaches the forecast period. In other words, the forecaster obtains

more and more information as he or she approaches the forecast period starting date

and this is taken into account in deriving the proxy.

We include the derived expected variance of both real GDP growth and inflation

(PY and PI).

4 Do uncertainty proxies measure uncertainty?

As stated in Proposition 1, we expect appropriate proxies to respond to exogenous

shocks to uncertainty. Furthermore, referring to Proposition 2, we have reasons to

believe that uncertainty in all macroeconomic variables should be positively corre-

lated.

4.1 Narratives

In order to evaluate alternative uncertainty proxies we rely on the idea that an ap-

propriate uncertainty proxy should react to an unforeseen event that is considered

to either increase or decrease uncertainty exogenously. The advantage of this ap-

proach is that we need not assume that e.g. probability forecast proxies are the true

60_____________________________________________________________________________________A Critical Look at Measures of Macroeconomic Uncertainty

uncertainty measures and proceed to evaluate other proxies based on their affinity

with this type of proxy. Instead, we assume that uncertainty proxies should increase

with some unforeseen and exogenous events at certain dates. If this is not the case

the proxies are bad uncertainty measures. Our narrative approach relies on iden-

tifying dates, corresponding to months or quarters, where uncertainty increased or

decreased.6

For comparison purposes, we restrict our attention to the time period 1987-2005

for which all but the probability forecast proxies are available. The choice of dates

is subjective by nature, but we have carefully applied the following criteria. First,

the event should be such that when it occurs, it more or less instantaneously creates

a change of uncertainty in a particular direction. Second, it should be exogenous to

the variable subjected to the test. We construct three sets of dummy variables. One

is a dummy variable for military conflicts, CONFLICT , that includes two terrorist

attacks and one military conflict. These episodes are also included in Chen and

Siems (2004), where the authors study how returns of stocks have evolved during

periods of military conflicts. One is a financial dummy, FINCRISIS, that in-

cludes two financial crises, and one is a dummy for regular US presidential elections,

ELECTION , that includes five events. The episodes and dates are displayed in

Table 4.

Table 4: Periods of shocks to uncertainty

CONFLICT FINCRISIS ELECTIONOct 19 1987 Black Monday

Nov 8 1988Aug 2 1990 Iraq invasion

Nov 3 1992Feb 26 1993 WTC bombing

Nov 5 1996March 10 2000 Dot Com crash

Jan 6 2001Sep 11 2001 Terror attacks

Nov 2 2004

6In this paper, we use an identification strategy by choosing dates that should represent shocksto uncertainty. An alternative, but much more difficult, strategy would be to measure the arrivalrate and signal quality of incoming information. The more information we acquire and the betterthe information is, the less uncertain we are. Imagine a person reporting a probability forecastdistribution of the weather tomorrow and then moving into a room without windows and no contactwith the outside world. After a few days, a new probability forecast distribution is reported.Supposedly, the mean is unchanged but the variance of the distribution has increased!

_____________________________________________________________________________________61

To most people, the terrorist attacks on September 11 2001 should constitute

an event that must instantaneously have raised uncertainty. Bartram, Brown, and

Hund (2005) find evidence of an increase in the systematic component of risk and

Bloom (2006) documents a dramatic increase in the number of times the wording

"uncertainty" was used in the FOMC meetings right after the 9/11 attacks. These

findings support the idea that uncertainty increased sharply with the 9/11 terrorist

attacks.

The financial crisis episodes in October 1987 and March 2000 are endogenous

to the volatility proxies and therefore only included as controls in these regressions.

No such problem should exist for the other proxies and we expect that all proxies

should increase with these events as people were likely to become uncertain about

the future performance of the economy, given such large disruptions of the stock

market.7

The presidential election outcomes are different from the other episodes. Al-

though the presidential elections occur on regular dates, the outcome is unknown

beforehand. When the outcome of the election becomes known, this implies a reduc-

tion of uncertainty, thus satisfying our first criterion of selection.8 Furthermore, the

outcomes of presidential elections can be said to comply with our second criterion,

exogeneity, since uncertainty does not affect the date of resolved uncertainty.

To test whether proxies of uncertainty have reacted as expected to these types of

events, we run the following regression for each of the considered uncertainty proxies

(UPt),

UPt = c+βLAGUPt−1+βCCONFLICT +βFFINCRISIS+βEELECTION+εt,

(9)

where one lag of the proxy is included to purge the series of a predictable autore-

gressive component in the evolution of proxies.9 We expect βC and βF to be positive

and βE to be negative.10

Table 5 indicates that we seem to have been quite successful in identifying dates

of increased uncertainty, CONFLICT and FINCRISIS. The presidential election

dummy, on the other hand, does not come in significant in any of the regressions.

7As expressed by Fed Governor Phillips (1997): "Such episodes [stock market crashes] aregenerally accompanied by dramatic increases in uncertainty".

8Naturally, election polls might indicate how uncertain the outcome is. This issue is ignoredin this analysis and the negative shocks to uncertainty at the resolve of uncertainty are treatedequally across elections.

9For quarterly measures, the dummies are lagged one period to ensure that the effect of theevent at the time of the survey is picked up by our estimates.

10The estimated parameters for the dummy variables will simply tell us if the unpredictablecomponent in the proxy is significantly different from non-dummy periods.

62_____________________________________________________________________________________A Critical Look at Measures of Macroeconomic Uncertainty

However, if we look at daily data of VO (implied volatility) in Figure 1, it is clear

that for all elections except in the year 2000, the volatility decreased the day after the

election. For the 2000 election, the volatility increased the day after the election,

but we should note that the election outcome was not known at that time. The

day after the decisive meeting in Congress on January 6 2001, volatility decreased.

Further, VO exhibits a highly significant and positive sign on CONFLICT . These

findings support the use of VO as a suitable proxy of uncertainty.

Table 5: Dummy regression results

UP CONFLICT FINCRISIS ELECTION Old R2 New R2 ObsDMB -** +*** - 0.76 0.77 222DMF + - - 0.18 0.17 222DMD + + + 0.01 0.01 222DMU + + + 0.59 0.54 222DML +* +** + 0.75 0.75 222DMV +* +*** - 0.64 0.66 222DMH +* + - 0.73 0.73 222DMR + - + 0.80 0.80 222

VO +*** (+***) - 0.76 0.82 222VH + (+***) + 0.89 0.91 222

DSY + +** - 0.06 0.13 74DSC +*** +** + 0.13 0.28 74DSP + - + 0.34 0.30 74DSU +*** - - 0.29 0.39 74DSH +*** + - 0.22 0.31 74DSI +** + + 0.19 0.22 74DSR + - - 0.17 0.19 74

PY - + + 0.08 0.07 55PI + + - -0.02 -0.06 55

Note: The table only presents the sign of the estimated coefficients, as the size is not comparable

across proxies. Old R2 is the r-square of the regression of equation 9, excluding the dummies. New

R2 is the r-square when including the dummies. Obs is the number of observations. *, ** and ***

denote 10, 5 and 1 percent significance levels.

_____________________________________________________________________________________63

Figure 1: Daily implied volatility (VO) around US presidential elections 1992-2004Note: The solid line indicates the election date (11/3/1992, 11/5/1996, 11/7/2000 and

11/2/2004. The dashed line indicates the certification of the electoral vote in Congress 1/6/2001)

64_____________________________________________________________________________________A Critical Look at Measures of Macroeconomic Uncertainty

For the Michigan consumer survey proxies, it is the proxy DMV, disagree-

ment concerning buying condition for vehicles, that seems to be the best indicator.

This is because of its positive and significant estimates of both CONFLICT and

FINCRISIS, as well as some increase in the adjusted R-squared when the dummies

are included. For the survey of professional forecaster, DSC, disagreement concern-

ing real consumption, seems to be the most appropriate proxy of uncertainty. It has

highly significant coefficient estimates for both CONFLICT and FINCRISIS, as

well as a large increase in the adjusted R-squared.

The probability forecast proxies, PY and PI, do not pick up any changes in

uncertainty at the dummy dates. This is surprising, given that these proxies are

often believed to be more refined proxies of uncertainty. A possible reason could be

that the sample period is somewhat shorter than for the other proxies. Nevertheless,

this finding casts some doubt on the usefulness of these proxies of uncertainty.

Thus, the narrative evidence indicates that most survey based proxies and the

volatility proxies have reacted as expected to exogenous shocks to uncertainty, while

the probability forecast proxies show strikingly weak responses to these shocks.

4.2 Correlations

The Pearson’s correlation coefficients between all considered proxies are illustrated

in Figure 2.

Figure 2: Correlations of all uncertainty proxiesNote: Numbers are Pearson correlation coefficients, with stars indicating that the estimate issignificantly different from zero at the 1 percent significance level. The grey boxes show threegroups of uncertainty proxies that have mainly positive intercorrelations within each group.

_____________________________________________________________________________________65

Indeed, a large share of the correlations is positive. Out of 171 correlations,

70 are significantly positive at the one percent level, as indicated by *. Only ten

correlations are significantly negative. Generally, the disagreement proxies from

the Michigan Consumer Survey and the Survey of Professional Forecasters survey

data show rather high and significant correlations, both within and between groups.

There are two exceptions. DMD, disagreement concerning real family income, is

predominantly negatively correlated with the other proxies, with seven out of 18

correlations being significantly negative. DMB, disagreement about the business

conditions, is positively correlated with DMD and negatively correlated with a few

other proxies. The results here thus indicate that DMD and DMB do not capture

the same phenomenon as the other proxies.

The correlation coefficients between the disagreement proxies and the other prox-

ies are mostly insignificant. Only four out of 60 correlations are significantly positive

at the one percent level. This result is very different from the positive relation be-

tween probability forecast proxies and disagreement proxies found in Zarnowitz and

Lambros (1987). The reason for this finding could be that the two sample periods are

not overlapping, but also that our study addresses the problem of different forecast

horizons as explained above. Finally, the non-disagreement proxies, the volatility

and probability forecast proxies, exhibit a significant and positive correlation with

each other.

Thus, within the groups of proxies, indicated by shaded areas, the correlation

table supports both Proposition 1 and 2. As expected, we see positive correlations

across variable-specific uncertainty proxies. However, the two groups seem to give

different answers to how uncertainty varies over time.

5 Factor analysis

In section 2, we concluded that any proxy of uncertainty could be driven by many

underlying factors, or sources of uncertainty. In this section, we investigate how

many underlying common factors that are suggested by the data reduction tech-

nique known as factor analysis.11 For a complete description of factor analysis, see

Sharma (1996) and Johnson (1998). Factor analysis is performed on each of the

subgroups constituted by the Michigan Consumer Survey and the Survey of Pro-

fessional Forecasters. Common factors are searched for across variables, using the

same proxy type, to avoid problems of mixing different types of proxies. For the

probability forecast proxies and the volatilities, there are only two proxies of each

11Entia non sunt multiplicanda praeter necessitatem!

66_____________________________________________________________________________________A Critical Look at Measures of Macroeconomic Uncertainty

and no factor analysis is conducted.

The purpose of factor analysis is to search for underlying latent factors that

explain co-movements in different variables. The number of common factors can in

general be as many as the number of variables less one. The factor analysis provides

us with some useful results. First, it can help us identify which proxies are more

closely connected to any common factors, and which proxies are more idiosyncratic.

Second, it turns out that we detect and compute only one common factor for each

subgroup, and we interpret this factor as some general macroeconomic uncertainty.

Third, this common factor will be used for applications in section 6. Below, these

steps are described in more detail.

The Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy is used to de-

termine the appropriateness of performing factor analysis on the data. No formal

statistical test is available, but an overall KMO-value of 0.60 is the recommended

minimum value.12 We also restrict individual KMO-proxies to be above 0.50 for

inclusion in the common factor extraction. If any proxy is below 0.50, this proxy is

excluded. We rerun the KMO-test until all separate proxies are above 0.50 so that

all idiosyncratic proxies are excluded.13 For Michigan Consumer Survey proxies,

we must first disqualify DMU, disagreement concerning unemployment, and then

DMB, disagreement about business conditions, because of individual KMO-values

lower than 0.50. Referring to Table 5, the narrative evidence also indicates that

DMU and DMB are weak proxies for uncertainty. For the Survey of Professional

Forecasters proxies, we find strong results for the KMO test with no values below

0.80. Overall, the average KMO-value is 0.74 for the Michigan Consumer Survey

group and 0.86 for the Survey of Professional Forecasters group after exclusion of

DMU and DMB, which indicates that the remaining proxies are well suited for factor

analysis. All variables with their respective KMO-values and average KMO-values

for the two subgroups are displayed in Table 6.

Next, we estimate factor models, one for each subgroup, by principal axis factor-

ing (PAF) to determine how many factors are suggested by this formal procedure.14

The eigenvalues of the sample covariance or correlation matrix measures the strength

of the factors in explaining the total variance in all variables. According to the often

employed larger-than-one-eigenvalue criterion, as well as a screeplot analysis, there

12A KMO-value of below 0.50 is deemed "unacceptable", 0.50-0.59 "miserable", 0.60-0.69"mediocre", 0.70-0.79 "middling", 0.80-0.89 "meritorious and 0.90-1.00 "marvelous" (see Sharma(1996) p. 116).

13Referring to the model in Section 2, these excluded proxies can be seen as representing thosevariables in the economy that do not enter endogenously in the VAR.

14Alternative methods such as Iterated Principal Factors and Maximum Likelihood give verysimilar results.

_____________________________________________________________________________________67

Table 6: Kaiser-Meyer-Olkin values for sampling adequacyUncertainty proxy KMO

DMF 0.78DMH 0.66DMR 0.74DML 0.71DMD 0.90DMV 0.75

Michigan Consumer Survey average 0.74

DSP 0.86DSI 0.86DSH 0.81DSC 0.96DSY 0.89DSR 0.92DSU 0.80

Survey of Professional Forecasters’ average 0.86

is exactly one common factor each for the Michigan Consumer Survey and the Sur-

vey of Professional Forecasters subgroups. The eigenvalues above zero are displayed

in Table 7. The fact that we only detect one common factor for each subgroup

indicates that there is one prime driver of uncertainty common to all proxies, which

can be interpreted as some general macroeconomic uncertainty.

Table 7: Eigenvalues for the number of common factorsFactors Michigan Consumer Survey Survey of Professional Forecasters1 2.36 4.042 0.42 0.303 0.04 0.07

With one factor for each subgroup, we take a look at the factor loadings of each

proxy. It turns out that for the Michigan Consumer Survey subgroup, DMD, the

disagreement about future real family income, is negatively related to the common

factor but positively related to all others. DMD was also considered to be a weak

proxy of uncertainty judging from the narrative evidence in Table 5. That DMD has

the lowest communality indicates that the negative loading for this factor is signifi-

cant but small. Furthermore, DMD seems quite closely related to DMB, according

to the correlation coefficient reported in 2, and is somewhat guilty by association to

DMB. Thus, although formally not disqualified, DMD must be considered a weak

proxy for uncertainty. DML, which refers to disagreement about buying conditions

68_____________________________________________________________________________________A Critical Look at Measures of Macroeconomic Uncertainty

for large goods, has the highest communality with the common factor and DMD

the lowest. DML also seem to be an adequate proxy by looking at Table 5. For

the Survey of Professional Forecasters proxies, all factor loadings are positive. DSY,

disagreement concerning real GDP, has the highest communality and DSP, disagree-

ment concerning corporate profits, the lowest. The narrative evidence in Table 5

also indicate that DSY is a better proxy than DSP.

Finally, to get an estimate of the underlying factor, we need to score the data to

produce an estimate of the latent common factor. The scoring coefficients help form

the weights put on each variable so we can produce an estimate of the underlying

factor at time t. We interpret this factor as an estimate of general macroeconomic

uncertainty. The factor loadings, variance contributions and the scoring coefficients,

using the regression method, are reported in Table 8.15

Table 8: Loadings, variance decompositions and scoring coefficientsFactor loading Communality Uniqueness Scoring coeff.Michigan Consumer Survey

DMF 0.65 0.42 0.58 0.15DMH 0.47 0.23 0.77 0.11DMR 0.57 0.32 0.68 0.11DML 0.85 0.73 0.27 0.47DMD -0.36 0.13 0.87 -0.06DMV 0.73 0.53 0.47 0.27

Survey of Professional ForecastersDSP 0.46 0.21 0.79 0.05DSI 0.82 0.67 0.33 0.17DSH 0.84 0.71 0.29 0.25DSC 0.72 0.52 0.48 0.11DSY 0.87 0.76 0.24 0.31DSR 0.79 0.62 0.38 0.14DSU 0.74 0.55 0.45 0.11

The computed factors are weighted combinations of the included proxies. The

common factor for the Survey of Professional Forecasters proxies (SFactor) contains

all the Survey of Professional Forecasters proxies, but DSY, real GDP disagreement,

contributes the lion’s share followed by DSH, disagreement concerning buying con-

ditions for houses, and DSI, CPI-inflation disagreement. The common factor for

the Michigan Consumer Survey proxies (MFactor) contains all proxies but DMU

and DMB and assigns the largest weight to DML, disagreement concerning buying

conditions for large goods, followed by DMV and DMF.

15The alternative Bartlett scoring method yields nearly identical results.

_____________________________________________________________________________________69

In this section, we have reduced our survey based disagreement proxies of un-

certainty from 15 (eight from the Michigan Consumer Survey and seven from the

Survey of Professional Forecasters) to two, MFactor and SFactor. In the process,

we have excluded those few proxies that are considered to be most idiosyncratic

(DMU and DMB) and have assigned larger weights to those that are closely con-

nected to the others. Thus, we believe that these two factors could be reasonable

conceptions of the general macroeconomic uncertainty in the economy as captured

by disagreement.

6 Extensions

The correlation table, the narrative evidence, and the factor analysis helped us

evaluate uncertainty proxies. In this section, we will look more closely at how un-

certainty proxies co-move with the business cycle and thereafter we study if uncer-

tainty is of importance for aggregate consumption and residential investment. We

use our factors for the Michigan consumer survey group (MFactor) and the survey

of professional forecasters (SFactor) along with volatility proxies (VO and VH) and

probability forecast proxies (PY and PI).

6.1 Co-movements with the business cycle

The relation between business cycles and uncertainty is largely left unexplored in

the previous literature. Some papers relating macroeconomic uncertainty to the

business cycle are Ball (1992) and Shields, Olekalns, Henry, and Brooks (2005). Ball

(1992) analyzes the relation between inflation and inflation uncertainty and argues

that higher inflation should raise inflation uncertainty. Shields, Olekalns, Henry, and

Brooks (2005) find that uncertainty about inflation and output increases with shocks

to output and inflation. We provide some empirical evidence on the co-movement of

uncertainty with the business cycle in general by comparing the time series evolution

of uncertainty proxies with the real GDP-gap.

The plots of proxies of uncertainty and the business cycle is shown in Figure

3.16 Looking at the co-movements of the business cycle and the proxies, it appears

as if uncertainty seems to be higher the further we are from the "normal" state of

the economy. Looking at the official NBER business cycle dates, it appears as if

uncertainty has been higher at the turn of the business cycle moving away from a

16The business cycle measure is obtained by standard Hodrick—Prescott (HP) filtering of thelog real output with a smoothing weight set to 1600. The Michigan Consumer Survey measuresand volatility measures have been converted from monthly to quarterly by averaging.

70_____________________________________________________________________________________A Critical Look at Measures of Macroeconomic Uncertainty

recession.17 For the probability forecast measures PY and PI, these findings are not

as clear.

Figure 3: The Business Cycle and Uncertainty Proxies 1980-2005Note: Displayed are the GDP HP-filtered business cycle (RHS) and selected uncertainty proxies(LHS). MFactor, SFactor, VO and VH have been normalized to 100 at their respective firstobservation. NBER peak to recession periods are displayed as shaded areas and cover thefollowing peak-through periods: January 1980-July 1980, July 1981-November 1982, July1990-March 1991, and March 2001-November 2001. Source: www.nber.org/cycles.html

17Peak-Through: January 1980-July 1980, July 1981-November 1982, July 1990-March 1991,March 2001-November 2001. Source: www.nber.org/cycles.html

_____________________________________________________________________________________71

To further explore the relation between the business cycle and uncertainty Table

9 shows the correlations between the absolute value of the GDP-gap and uncertainty

proxies.18 All uncertainty proxies have positive correlation coefficients, in particular

the survey based proxies, SFactor and MFactor, show strong correlations.

Table 9: Correlations of uncertainty proxies with the business cycleUP Corr(UP, |GDPgap|)

MFactor 0.44SFactor 0.49VO 0.26VH 0.15PY 0.33PI 0.20

6.2 Precautionary savings

Next, we estimate Euler equations following Campbell and Mankiw (1991), which

allow for precautionary savings effects on consumption, ∆ct, through an uncertainty

proxy, UPt,

∆ct = α+ β1rt−1 + β2∆ydt−1 + γcUPt−1 + εt. (10)

The log change in disposable income, (∆ydt), is added to control for hand-to-mouth

behaviour of consumers. When we estimate equation (10), the uncertainty proxy,

the real interest rate (r), and the disposable income must be instrumented due to

time aggregation issues. Our instruments are lagged values of ∆c, ∆yd, r and UP .19

The precautionary savings effect would show up as a significantly positive γc,

meaning that high uncertainty would lead to consumption being postponed into the

future. It might seem counter-intuitive to expect a positive effect on∆ct from UPt−1,

but as the contemporaneous consumption level decreases with higher uncertainty,

the change in consumption to the next period increases ceteris paribus.

The results from our two-stage least squares regressions, shown in Table 10,

indicate mixed results for our set of uncertainty proxies. The Survey of Professional

Forecasters factor (SFactor) is significant at the five-percent level. The Michigan

Consumer Survey disagreement factor (MFactor) is negative, but insignificant. The

VO and VH volatility proxies show no significant effects. For the probability forecast

18The GDP-gap is measured as the absolute real percentage deviation of GDP from its HP-trend(w=1600).

19See Hall (1988) for further motivation. The lag structure follows Hall (1988) and Campbelland Mankiw (1991).

72_____________________________________________________________________________________A Critical Look at Measures of Macroeconomic Uncertainty

Table 10: Estimates of the consumption Euler equationr ∆yd UP R2 Obs

MFactor 0.028 0.236 -0.166 -0.07 97(0.83) (1.02) (-1.13)

SFactor -0.018 0.298 0.308** -0.02 91(-0.57) (1.59) (2.58)

VO -0.016 0.268 0.010 -0.03 73(-0.67) (1.26) (1.03)

VH -0.007 0.439*** 0.021 -0.28 97(-0.25) (2.84) (-0.59)

PY -0.009 0.043 -0.016 -0.12 53(-0.28) (0.18) (-0.69)

PI -0.012 -0.096 -0.037* -0.16 53(-0.55) (-0.43) (-1.69)

Note: *, ** and *** denote 10, 5 and 1 percent significance levels.

measures PY and PI, the estimates are negative, with the one for PI significant at

the ten-percent level.

6.3 Residential investment

Finally, following Downing and Wallace (2005), we study how uncertainty influences

the decision to invest in residential housing. Uncertainty is expected to decrease in-

vestment, due to the increased value-to-wait when uncertainty is high. See Bernanke

(1983) on uncertainty and the irreversibility of investment.

For all qualified proxies, we estimate an extension of the model in Downing and

Wallace (2005) adding UPt,

Startst = β0 + β1HRt + β2TRt + β4HRvolt + β5TRvolt

+γrUPt + controls+ εt, (11)

where Startst is the number of housing starts for quarter t. HRt is housing returns;

TRt is the T-bill rate; HRvolt is the historical volatility of housing returns and

TRvolt is the volatility on the T-bill rate. The controls are the spread between

the thirty-year and the ten-year bond yields and a set of seasonal dummies. The

estimation technique is adapted to the dependent variable being an integer count

variable. In particular, we use the Poisson based estimation technique as described

in Greene (2003).

Downing and Wallace (2005) use HRvolt as their only proxy of uncertainty but

we find that the reported negative sign for this proxy is unstable over subperiods.

_____________________________________________________________________________________73

The results when adding uncertainty proxies are shown in Table 11. The sign on

the uncertainty proxy is negative and significant for all but the probability forecast

proxies PY and PI. This constitutes further support for survey proxies of uncertainty

(except PY and PI), given that uncertainty should decrease the number of housing

starts.

Table 11: Estimates of the residential investment decisionHR TR HRvol TRvol UP R2 Obs

MFactor 0,016*** -0,029*** 0,019 0,055** -0,137*** 0,87 102(5,6) (-6,33) (1,64) (2,16) (-6,06)

SFactor 0,025*** -0,033*** -0,0001 -0,03 -0,059** 0,81 98(6,7) (-6,87) (-0,01) (-1,14) (-2,45)

VO 0,024*** -0,049*** -0,019 -0,103*** -0,005*** 0,82 80(5,32) (-11,63) (-1,03) (-4,38) (-3,01)

VH 0,027*** -0,036*** -0,016 -0,04 -0,012* 0,8 104(7,69) (-8,99) (-0,99) (-1,55) (-1,68)

PY 0,016*** -0,031*** 0,032** -0,074*** 0,031 0,81 56(3,29) (-4,52) (2,00) (-2,89) -0,22

PI 0,016*** -0,030*** 0,031* -0,078*** 0,192 0,81 56(3,2) (-3,99) (1,84) (-3,30) (0,93)

Note: *, ** and *** denote 10, 5 and 1 percent significance levels.

7 Conclusions

The main purpose of this paper is to evaluate available proxies of uncertainty. Using

a simple VAR-model of the economy, we derive two propositions. The first propo-

sition states that different proxies of uncertainty should react with the same sign

to large exogenous shocks to uncertainty. The second states that, under reason-

able assumptions, various uncertainty proxies should be positively correlated. We

use these criteria to evaluate proxies of uncertainty. To apply the first criterion we

identify dates that should increase or decrease uncertainty. To apply the second,

we use correlation analysis. Further, using factor analysis, we investigate how many

factors of uncertainty that are common across different proxies. Finally, we include

proxies of uncertainty in standard macroeconomic applications where uncertainty is

supposed to be of importance.

We show that stock market volatility proxies behave as expected when there are

exogenous shocks to uncertainty and are also of importance for residential invest-

ment decisions. Therefore, we find some support for the use of volatility proxies

as indicators of uncertainty. This is especially true for the implied volatility proxy

74_____________________________________________________________________________________A Critical Look at Measures of Macroeconomic Uncertainty

derived from option prices.

A notable finding in this paper is the weak support for the probability forecast

proxies as indicators of uncertainty. The narrative evidence gives little indication

that this type of proxy is picking up uncertainty. Moreover, in applications where

uncertainty is likely to be of importance, these proxies do not add any explanatory

power.

The disagreement proxies pick up exogenous shocks to uncertainty and are also

of importance for economic decisions. The strongest support is given to the use of

disagreement proxies based on quantitative surveys. Zarnowitz and Lambros (1987)

and Giordani and Söderlind (2003) also claim that disagreement proxies are viable

proxies for true uncertainty. However, the crucial assumption made by Zarnowitz

and Lambros (1987) to draw this conclusion is that true uncertainty is equal to

the probability forecast variance. Our paper indicates that such a supposition is

incorrect. Giordani and Söderlind (2003) instead use an asset pricing model to

evaluate disagreement proxies but have the same problem since they rely on time

series model proxies of uncertainty as the true measure of uncertainty.

From the correlation between proxies of uncertainty, we find that there are two

independent groups. One group consists of the survey disagreement proxies; the

other consists of the probability forecast and stock market volatility proxies. Most

proxies are positively correlated within groups. This result is reinforced by factor

analysis through which we find that all proxies from the Survey of Professional

Forecasters and most proxies from the Michigan Consumer Survey are tied together

by exactly one common factor for each survey. By the factor analysis, we are able

to the compute common factors, supposedly representing uncertainty, that drive the

different proxies. These factors are taken to be indicators of general macroeconomic

uncertainty.

We also find that proxies of uncertainty to be positively correlated with the

absolute value of a business cycle measure. The further away from a "normal"

state of the economy we are, the higher is the uncertainty. The co-movement of

uncertainty and the state of the economy could be an important factor in the business

cycle, as well as in policy making, and has previously remained undetected in the

literature.

_____________________________________________________________________________________75

References Aguilar, Javiera, and Peter Hördahl, “Option Prices and Market Expectations”, Riksbank

Quarterly Review 1999:1, p. 43-70. Ball, Lawrence, “Why Does Higher Inflation Raise Inflation Uncertainty?”, Journal of

Monetary Economics 29, 1992, p. 371-378. Bartram, Söhnke M., Gregory W. Brown, and John E. Hund, “Estimating Systemic Risk

in the International Financial System,” FDIC CFR Working Paper 2005-12, 2005. Bernanke, Ben S., “Irreversibility, Uncertainty, and Cyclical Investment” The Quarterly

Journal of Economics 98, 1983, p. 85-106. Bloom, Nicholas, “The Impact of Uncertainty Shocks: Firm Level Estimation and a

9/11 Simulation”, Center for Economic Performance Discussion Paper 718, 2006. Bomberger, William A., “Disagreement as a Measure of Uncertainty”, Journal of

Money, Credit, and Banking 28, 1996, p. 381-392. Campbell, John Y., and N. Gregory Mankiw, “The Response of Consumption to

Income: A Cross-Country Investigation”, European Economic Review 35, 1991, p. 723-767.

Chen, Andrew C., and Thomas F. Siems, “The Effects of Terrorism on Global Capital

Markets”, European Journal of Political Economy 20, 2004, p. 349-366. Downing, Chris, and Nancy Wallace, “An Empirical Investigation of Housing

Investment under Uncertainty,” Jones Graduate School of Management, Rice University and Haas School of Business, University of California at Berkeley, 2005.

Giordani, Paolo, and Paul Söderlind, “Inflation Forecast Uncertainty”, European

Economic Review 47, 2003, p. 1037-1059. Greene, William H., Econometric Analysis, Prentice Hall, Upper Saddle River, New

Jersey, 2003. Hall, Robert E., “Intertemporal Substutution in Consumption”, The Journal of Political

Economy 96, 1988, p. 339-357. Hassler, John, “Risk and Consumption”, Swedish Economic Policy Review 3, 1996. Johnson, Dallas E., Applied Multivariate Methods for Data Analysts, Duxbury Press,

1998.

76_____________________________________________________________________________________A Critical Look at Measures of Macroeconomic Uncertainty

Lyhagen, Johan, “The Effect of Precautionary Saving on Consumption in Sweden”, Applied Economics 33, 2001, p. 673-681.

Phillips, Susan M., “Black Monday: 10 Years Later,” Speech at Bentley College,

October 15, 1997. Romer, Christina. D., “The Great Crash and the Onset of the Great Depression”, The

Quarterly Journal of Economics 105, 1990, p. 579-624. Sepulveda, Jean, “The Relationship Between Macroeconomic Uncertainty and the

Expected Performance of the Economy”, North Carolina State University, 2003. Sharma, Subhash, Applied Multivariate Techniques, John Wiley & Sons, Inc.,

University of South Carolina, 1996. Shields, Kalvinder, Nilss Olekalns, Ólan. T. Henry, and Chris Brooks, “Measuring the

Response of Macroeconomic Uncertainty to Shocks”, The Review of Economics and Statistics 87, 2005, p. 362-370.

Zarnowitz, Victor, and Louis A. Lambros, “Consensus and Uncertainty in Economic

Prediction”, Journal of Political Economy 95, 1987, p. 591-621.

_____________________________________________________________________________________77

Essay 3

Can Endogenous Monetary Policy Explain the Deviations from UIP

1 Introduction

Numerous empirical studies have found that nominal exchange rates of countries

with high interest rates appreciate rather than depreciate as expected from uncov-

ered interest parity (UIP). It is probably fair to say that traditional explanations

in terms of time varying risk premia and/or systematic forecast errors have failed

to explain this phenomenon. Tentative evidence however suggests that the typi-

cal finding of a negative relationship between exchange rate changes and interest

rate differentials is confined to short-term interest rates. The few available studies

of UIP for long-term interest rates report slope coefficients from regressions of ex-

change rate changes on interest rate differentials (henceforth βUIP -coefficients) that

are positive and often insignificantly smaller than unity (Alexius, 2001, Meredith

and Chinn, 1998). Short-term interest rates differ from other asset prices (including

long-term bond rates) in that they constitute the main monetary policy instrument

in most industrialized countries with flexible exchange rates. This paper explores

the possibility that the negative relationship between short-term interest rates and

ex post exchange rate changes emerges as the economy including monetary policy

responds to shocks.

The idea that the negative co-movements of exchange rates changes and interest

rate differentials could be a consequence of the monetary policy response to shocks is

originally due to McCallum (1994). He uses a two equation framework to show that a

negative relationship emerges if the central banks stabilize the nominal exchange rate

in the face of autocorrelated shocks to the exchange rate risk premium. Meredith and

Chinn (1998) incorporate supply and demand equations, calibrate their model and

show that it may generate negative βUIP−coefficients in standard UIP tests giventhat an extremely high variance is assigned to the exchange rate risk premium. The

results in McCallum (1994) and Meredith and Chinn (1998) hence hinge crucially on

existence of large and variable shocks to the exchange rate risk premium, which is a

well-known way of obtaining negative βUIP -coefficients in UIP tests (Fama, 1984).

However, models of endogenous exchange rate risk premia have failed to generate

sizable predictable excess returns.

If it really is the endogenous response of monetary policy to shocks that gener-

ates negative βUIP -coefficients in UIP tests, this mechanism should be present not

only in models constructed for the purpose of explaining the exchange rate risk pre-

mium puzzle, but in open economy macro models in general. We use the Svensson

(2000) model to generate artificial time series on exchange rate changes and interest

rate differentials. The standard UIP test is applied to the resulting data sets and

the βUIP−coefficients are analyzed. The model parameters are then varied in order

_____________________________________________________________________________________81

to identify the conditions under which large, negative βUIP−coefficients can be ob-tained from the model even though it contains an ex ante UIP relationship with a

risk premium shock. We find that negative and large βUIP -coefficients emerge for

realistic parameter values when the central bank engages in interest rate smoothing.

There is considerable evidence that central banks do smooth interests (Woodford,

2003).

The mechanisms behind the deviations from UIP are analyzed in several different

ways. Impulse response functions of exchange rates and interest rates reveal that

there is always a period during which the domestic interest rate is higher than

the foreign interest rate while the exchange rate is appreciating in response to a

risk premium shock. This effect is more or less pronounced relative to other co-

movements between the two variables depending on parameter values. There are

realistic sets of parameter values for which the model generates βUIP -coefficients

below -3.

Following Fama, the deviations from UIP are also analyzed in terms of decom-

positions focusing on the variance of the risk premium relative to other second

moments. These decompositions reveal that the Svensson model generates negative

βUIP -coefficients for parameter values where the variance of the interest rate differ-

ential is relatively small. This is in a sense consistent with Fama’s result that large

deviations from UIP require a small variance of expected exchange rate changes.

An advantage of using a full macroeconomic model to analyze the exchange rate

risk premium puzzle is that unobservable variables such as the variance of expected

exchange rate changes are determined endogenously within the model. We are hence

able to dig a little deeper into the mechanisms behind the deviations from UIP.

In order to evaluate whether the output from the model is reasonable in other di-

mensions, we compare the second moments of interest rate differentials, output, and

inflation to empirical counterparts. As indicated by the decompositions discussed

above, it turns out that large deviations from UIP only emerge when the variance

of the interest rate differential is small. This is probably partly due to the simplistic

modeling of the foreign country including foreign monetary policy as exchange rate

movements have opposite effects for the foreign economy and hence would induce

interest rate movements of opposite signs. Before turning to the Svensson (2000)

model the puzzle is briefly discussed in order to highlight why a macroeconomic

model is a useful tool for understanding the puzzle.

82_____________________________________________________________________________________Can Endogenous Monetary Policy Explain the Deviations from UIP

2 The puzzle

The standard test of UIP is to regress ex post exchange rate changes on lagged

interest rate differentials as in (1) and investigate whether [α, βUIP ] equals [0, 1].

Alternatively, a constant risk premium α is allowed and only the hypothesis that

βUIP equals unity is tested.

st+1 − st = α+ βUIP (it − i∗t ) + ξt+1. (1)

Since expected exchange rate changes are unobservable, (1) is a joint test of the

UIP hypothesis Et∆st+1 = it − i∗t and the rational expectation hypothesis st+1 =

Et[st+1] + ξt+1, where ξt+1 is white noise. If [α, βUIP ]6=[0, 1] in (1), UIP does nothold or the exchange rate expectations are systematically erroneous. The ex post

deviation from UIP in (1), ξt+1, can be divided into a risk premium ϕt+1 and a

forecast error νt+1:

ξt+1 = ϕt+1 + νt+1. (2)

As shown by Fama (1984), a small (below 0.5) or negative OLS estimate of βUIPin (1) implies that the variance of the risk premium exceeds the variance of the

expected exchange rate change:

Var¡ϕt+1

¢> Var (Et∆st+1) (3)

For instance, the typical finding that βUIP equals −3 in (1) requires that thevariance of the risk premium is at least four times as large as the variance of the

expected exchange rate changes (see Meredith, 2002). This is considered puzzling

because it is difficult to generate risk premia of the required magnitude. Numerous

unsuccessful attempts to model a large and variable exchange rate risk premium

have been made. Hodrick (1989) provides a survey of this literature.1

Several authors argue that the exchange rate risk premium puzzle is not as

puzzling as Fama (1984) and others have made it. For instance, Meredith (2002)

concludes that since the empirical failure of UIP is well documented, and it requires

that (3) is satisfied, the unobservable exchange rate risk premium must be large

and highly variable. If models of the risk premium have failed to capture this, it

must be the models rather than the facts that are erroneous. A full scale macro

1 A possible exception is De Santis and Gerard (1997, 1998), who are able to predict a non-trivial portion of the excess returns in foreign exchange markets using GARCH-models. Otherstudies have however failed to detect significant exchange rate risk premia in similar models basedon time-varying second moments (Giovannini and Jorion, 1989, Alexius and Sellin, 1999)

_____________________________________________________________________________________83

model allows us to focus on the right hand side of (3), i.e. the variance of expected

exchange rate changes. It can be argued that while it is difficult to generate a large

and highly variable risk premium, models of expected exchange rate changes have

not necessarily been more successful. Nominal exchange rate changes are notoriously

difficult to predict, especially at the short forecasting horizons that match short-term

interest rates (Meese and Rogoff, 1983). According to equation (3), the variance of

the risk premium has to be large relative to the variance of expected exchange rate

changes. This condition can be satisfied either if the variance of the risk premium

is large or if the variance of expected exchange rate changes is small. If nominal

exchange rate changes are completely unpredictable, as Meese and Rogoff (1983) and

others claim, the right hand side of (3) is zero and an infinitely small variance of the

risk premium is sufficient to satisfy the inequality in (3). Typically, little is known

about the unobservable expected exchange rate changes. A major advantage of using

a full scale open economy macro model rather than a partial equilibrium finance

model to analyze deviations from UIP is that expected exchange rates changes are

explicitly treated as endogenously determined within the model rather than just

assumed to follow exogenous stochastic processes.

3 The model

The Svensson (2000) model consists of a supply equation, a demand equation, a UIP

relationship and a monetary policy reaction function. Following Woodford (1996)

and Rotemberg and Woodford (1997), the following supply function is derived from

microfoundations in Svensson (2000):

πt+2 = αππt+1+(1− απ)πt+3|t+αy

£yt+2|t + βy(yt+1|t − yt+1)

¤+αqqt+2|t+εt+2. (4)

xt+τ |t denotes the rational expectation of the variable xt+τ conditional on the

information available at t. πt is the inflation rate, qt is the real exchange rate

defined as st + p∗t − pt, εt is a (cost push) supply shock, and yt is the output gap.

Demand for domestically produced goods is derived in Svensson (2000) and given

by

yt+1 = βyyt − βρρt+1|t + β∗yy∗t+1|t + βqqt+1|t + ηdt+1. (5)

y∗t denotes the foreign output gap and ηdt+1 is an i.i.d. demand shock. The long

real interest rate variable ρt is the sum of current and expected future short real

interest rates, measured as deviations from the natural real interest rate. The latter

84_____________________________________________________________________________________Can Endogenous Monetary Policy Explain the Deviations from UIP

is assumed to be constant and normalized to zero:

ρt =∞Xτ=0

¡it+τ − πt+τ |t

¢. (6)

The nominal exchange rate is determined by a UIP relationship:

it − i∗t = st+1|t − st + ϕt, (7)

where ϕt is the shock to the foreign exchange rate risk premium. The risk

premium follows an AR(1) process:

ϕt+1 = γϕϕt + ξϕ,t+1. (8)

For simplicity, the Foreign country is not modeled as elaborately as the Home

country. Foreign output and foreign inflation follow univariate AR(1) processes:

π∗t+1 = γ∗ππ∗t + ε∗t+1 (9)

and

y∗t+1 = γ∗yy∗t + η∗t+1. (10)

Furthermore, foreign monetary policy is assumed to be conducted according to

a Taylor rule:

i∗t = f∗ππ∗t + f∗y y

∗t + ξ∗it, (11)

where ξ∗it is the foreign monetary policy shock. The domestic central bank sets a

nominal short-term interest rate to minimize the expected value of the loss function

given all information available at t. The period t loss function contains up to four

arguments: domestic inflation squared, the output gap squared, the interest rate

squared and the change of the interest rate squared. For simplicity, possible target

levels for inflation, output, and the interest rate are hence set to zero. The weights

on up to three of the four arguments can be set to zero, i.e. output targeting,

interest rate targeting, and interest rate smoothing are possible but not necessary

characteristics of the model:

Lt = μπ2t + λy2t + θi2t + ζ (it − it−1)2 . (12)

_____________________________________________________________________________________85

The central bankminimizes the discounted expected value of Lt, i.e., Et

∞Pτ=0

δτLt+τ .

Its choice of an optimal short interest rate can be formulated as a linear regulator

problem. The model can be rewritten in state-space form and solved numerically for

specific parameters values using the algorithm presented in Oudiz and Sachs (1985).

This is discussed in detail in Svensson (2000).

In the discretionary monetary policy regime under consideration, the forward

looking variables xt = [qt, ρt,πt+2,t] are linear functions of the predetermined vari-

ables Xt = [πt, yt, π∗t , y

∗t , i

∗t , ϕt, y

nt , qt−1, it−1, πt+1|t]. Hence, xt = HXt where H is

endogenously determined. The solution to the model includes, among other things,

the optimal central bank reaction function. It shows how the short-term interest

rate is set as function of the predetermined variables:

it = fXt. (13)

This monetary policy rule is in practice rather similar to a Taylor rule, which is

why the welfare losses of following a rule of thumb rather than the optimal policy

are rather small. For instance, given the Svensson choice of parameter values, (13)

implies coefficients of 1.42 on inflation, 1.49 on the output gap, and 0.53 on the

lagged interest rate. In contrast to a simple Taylor rule, the central bank also reacts

to foreign inflation, foreign output gap, changes in the natural output and the risk

premium shock. All these coefficients are small (below 0.25) and several of these

other variables in the reaction function are unobservable. Hence the resulting mon-

etary policy is observationally similar to a Taylor rule. Given the optimal interest

rate rule and the resulting dynamics of the model, it can be used to generate time

series on e.g. interest rate differentials and exchange rate changes.

4 Calibration

The model contains 16 parameters: [απ, αy, αq, βy, β∗y, βρ, βq, f

∗π , f

∗y ,

γ∗π, γ∗y, γϕ, σ

2ε, σ

2d, σ

2ξi∗, σ

2ξiϕ]. Svensson (2000) does not actually estimate the open

economy model but selects reasonable parameter values. Table 1 shows his set of

parameter values as well as estimates from other studies using similar models. The

”realistic ranges” in the final row are set from the smallest to the largest value

encountered. Alternative parameter values are taken from Meredith and Chinn

(1998), (MC in Table 1), Rudebusch and Svensson (1999), (RS), Orphanides and

Wieland (1999), (OW), Batini and Haldane (1999), (BH), Smets (2000), (FS), and

Rudebusch (2000), (GR).

86_____________________________________________________________________________________Can Endogenous Monetary Policy Explain the Deviations from UIP

Table 1: Parameter estimates and ranges of realitistic valuesSource απ αy αq βy βq βρ γϕ rowLS (2000) 0.08 0.01 0.8 0.039 0.07 0.8 1MC (1998) 0.2 0.1 0.5 0.1 0.5 0.0 2RS (1998) 0.14 - 0.91 - 0.1 - 3OW (1999) 0.31-0.39 - 0.47-0.77 - 0.23-0.4 - 4BH (1999) - - 0.8 0.2 0.5 - 5PS (2000) 0.11-0.33 - 0.89-0.94 - 0.1-0.12 - 6FS (2000) 0.18 - - - 0.06 - 7GR (2000) 0.13 - 0.88 - 0.09 - 8range 0-1 0.08-0.39 0.01-0.1 0.47-0.94 0.039-0.2 0.06-0.5 0.0-0.8 9

απ captures the weight on lagged inflation relative to expected future inflation

in the Phillips curve in (4). The latter enters with a coefficient 1 − απ, i.e. the

coefficients on lagged and expected inflation sum to one. απ has been set to zero

(McCallum, 1997) as well as to unity (Svensson 1997) within this literature. The

smallest empirical estimate in Table 1, 0.47, is taken from Orphanides and Wieland

(1999).

αy is the effect of the output gap on inflation. The largest parameter value here,

0.39, stems from Orphanides and Wieland (2000).

αq and βq are the open economy parameters, capturing the effects of the real

exchange rate on supply and demand. Meredith and Chinn (1998) set these coeffi-

cients to 0.1 based on the IMFs model MULTIMOD for the G7 countries. Svensson

(2000) uses 0.01 for both αq and βq.

The output gap is highly autocorrelated in all studies. Smets (2000) obtain

the highest value of βy, 0.94. The Orphanides and Wieland (1999) value of 0.47

constitutes the lower bound of βy.

βρ is the interest rate sensitivity of demand. The smallest value, 0.06, is taken

from Smets (2000), closely followed by Svensson’s choice of 0.07. Meredith and

Chinn (1998) and Batini and Haldane (1999) use 0.5, which is the upper border of

the range of realistic parameter values for βρ. γϕ is the autocorrelation of the shocks

to the risk premium. This parameter is unobservable and has not been estimated

in this setting. Svensson (2000) uses the value 0.8 and Meredith and Chinn (1998)

choose 0.0. For the foreign parameters the Svensson values are used throughout.

Finally, the model contain five shocks, the variances of which are set to unity except

in the case of the foreign shocks that we set to zero in this application given the lack

of endogenous responses to shocks in the foreign economy.

_____________________________________________________________________________________87

5 Deviations from UIP in simulated data

By feeding independent, normally distributed shocks into (4), (5), and (8) artificial

time series on interest rate differentials and ex post exchange rate changes can be

generated from the model. For each set of parameter values, 1000 samples of 100

observations are created.2 The standard UIP test in (1) is then applied to the

simulated data and the average βUIP−coefficients are collected as the parametervalues are varied within the ranges defined in Table 1. The individual parameters

that have major effects on the resulting deviations from UIP are γϕ, απ, αy, βq, βρ,

and βy.

Four sets of simulations are performed in order to study the deviations from UIP

as functions of the parameter values. The benchmark parameterization is taken from

Svensson (2000). By altering the value of one parameter at a time we investigate how

the deviations from UIP respond to changes in each parameter. Second, we combine

the parameter values that yield the largest deviations from UIP in the first round

of simulations. A third set of otherwise identical simulations are performed with a

smoothing parameter included in the central bank loss function. In the fourth and

final set of simulations, each parameter is again set to the value that was shown to

yield the largest deviations from UIP in the third round. The results are presented

in the form of graphs of average βUIP as function of the parameter values.

The average βUIP using the Svensson (2000) calibration is 0.85, and none of

the simulations yield a negative estimate. The individual parameter with the most

obvious link to UIP deviations is the autocorrelation of the risk premium, γϕ. Figure

1a shows that higher autocorrelation monotonically lowers βUIP as γϕ is varied

from 0.00 to 0.95. The effect is particularly large as the autocorrelation of the risk

premium is increased from 0.7 to 0.9. The lowest average βUIP is 0.55 for γϕ equal

to 0.95. Increasing the autocorrelation of the exchange rate risk premium typically

but not always results in larger deviations from UIP (an exception can be seen in

Figure 2a).

The share of backward-looking versus forward-looking inflation expectations in

the Phillips curve, απ, is varied across the entire range 0.00 to 0.95. Figure 1b reveals

that βUIP is increasing in απ, especially for γϕ = 0.9. Hence the deviations from UIP

are larger the more forward looking the Phillips curve is. The second parameter of

the supply equation, αy, controls how much inflation is affected by the output gap.

This parameter is varied between 0.05 and 0.40, which encompasses typical values

from previous studies. Figure 1c shows that a lower αy results in larger deviations

2We generate samples of 200 observations and throw away the first 100 observations in order toremove dependence on starting values. An identical set of shocks are used across all simulations.

88_____________________________________________________________________________________Can Endogenous Monetary Policy Explain the Deviations from UIP

Figure 1: Average simulated UIP-Beta for different values of a specific modelparameter, Svensson (2000) model parameters

Figure 1a Autocorrelation of the risk premium shock

(γφ) Figure 1b

Share of lagged relative to expected future inflation in the Phillips curve (απ)

Figure 1c Effect of the output gap on inflation (αy)

Figure 1d

Effect of the real exchange rate on the output gap (βq)

Figure 1e Effect of the real interest rate on the output

gap (βρ)

Figure 1f Autocorrelation of the output gap (βy)

from UIP, but the effect is smallish.

The parameters βq, βρ, and βy control the effects on aggregate demand of the real

exchange rate, the real interest rate and the lagged output gap. Figures 1d to 1f show

that βUIP is decreasing in the two former and increasing in the autocorrelation of the

output gap. Higher autocorrelation of the risk premium leads to larger deviations

from UIP in these three cases. For γϕ = 0.9 βUIP typically falls to about 0.5.

The first set of simulations indicate that high autocorrelation of the risk pre-

mium shocks, a forward looking Phillips curve, a small effect of the output gap on

inflation, large effects of the real exchange rate and interest rate on demand, and

low autocorrelation of the output gap tend to produce large deviations from UIP.

All these mechanisms except a small αy increase the effects of a given change in

the interest rate on output and inflation, a hypothesis that will be investigated fur-

ther below. Clearly the effects of increasing or decreasing a particular parameter

value may vary depending on the other parameter values. Nevertheless, the main

impression from Figures 1a to 1f is that the deviations from UIP are small given the

_____________________________________________________________________________________89

Svensson (2000) set of parameter values.

Next we combine the parameter values that were shown to yield the lowest

average βUIP in Figures 1b to 1f. The default value of απ is therefore changed from

0.60 to 0.00, αy remains unchanged at 0.08, βq is increased from 0.039 to 0.20, βρ is

increased from 0.07 to 0.50, and βy is lowered from 0.80 to 0.47. This calibration is

referred to as "Minimum 1" in the tables and figures. When γϕ is set to 0.80 this

recalibrated model yields an average βUIP of -0.41 and the coefficient is negative in

89.4% of the 1000 simulations. To investigate the effects on βUIP of variations in

the parameters, we again vary one parameter at a time and plot against the average

βUIP for three different values of the autocorrelation of the risk premium: 0.70, 0.80,

and 0.90. The results are shown in Figures 2a to 2e.

Figure 2: Average simulated UIP-Beta for different values of a specific modelparameter, recalibrated model "Minimum 1" without smoothing

Figure 2a Share of lagged relative to expected future

inflation in the Phillips curve (απ) Figure 2b

Effect of the output gap on inflation (αy) Figure 2c

Effect of the real exchange rate on the output gap (βq)

Figure 2d Effect of the real interest rate on the output

gap (βρ) Figure 2e

Autocorrelation of the output gap (βy)

All parameters except αy retain a similar relationship to βUIP as in the bench-

mark calibration. Figure 2b shows that the relation between αy and βUIP is negative

in the recalibrated the model. Hence a larger effect of the output gap on inflation

may increase or decrease the deviations from UIP depending on the other parameter

values. Considerable deviations from UIP can be obtained from the model given this

90_____________________________________________________________________________________Can Endogenous Monetary Policy Explain the Deviations from UIP

calibration as βUIP approaches −0.5 in Figures 2a to 2e. This is nevertheless stillfar from the stylized fact of a slope coefficient of −3 in the standard test of UIP.It is well documented that the ability of models of endogenous monetary policy

to mimic actual monetary policy improves if the central bank is engaged in interest

rate smoothing. As the Svensson framework incorporates this possibility we change

the parameter ζ governing the disutility of interest rate changes in (12) from 0.0 to

1.0. All other parameter values remain the same as the previous set of simulations.

With the autocorrelation of the risk premium γϕ equal to 0.70 the average βUIPis −1.35 for this recalibrated specification with smoothing. 98.0% of the 1000 sim-

ulations yield a negative βUIP . As shown in Figures 3a to 3e almost all average

βUIP -estimates fall as smoothing is added to the model and the effect is often dra-

matic. While a higher autocorrelation of the risk premium typically increases the

deviations fromUIP the curves representing γϕ = 0.70 are often below the γϕ = 0.80-

curves. Hence the deviations from UIP are not simply functions of the variance of

the risk premium. As in Figure 2b but in contrast to Figure 1c, increasing the effect

of the output gap on inflation, αy, increases the deviations from UIP in Figure 3b.

The smallest average βUIP found in this round of calibrations is −2.21 given for afairly large effect of the output gap on inflation ( αy = 0.25).

The deviations from UIP are large throughout Figures 3a to 3e as βUIP falls

to −1.5 in most of these graphs. However, since the coefficients are still above thetypically observed value of −3 we continue to search for larger deviations from UIPby combining the individual parameter values behind the minima in Figures 3a to

3e while keeping interest smoothing in the central bank loss function. This results

in an average βUIP of −3.43.In Figure 4a αy or the effect of the output gap on inflation is varied for three

different values of the autocorrelation of the risk premium shocks. The largest

deviations from UIP are found for γϕ = 0.8 where βUIP falls below −3 for αy above

0.17. This is also observed for βq below 0.07 in Figure 4b. As it is now clear that

the model can produce βUIP -coefficients below −3 which per se is sufficiently lowto explain the puzzle we do not continue to search for even lower βUIP or larger

deviations from UIP in this recursive manner.

Table 2 sums up the simulation results. It contains the average βUIP , its standard

deviation, and the share of negative estimates in the four sets of simulations. Only

moderate deviations from UIP emerge for the Svensson (2000) parameter values.

When our six parameters are set to the value within the realistic range that yields

the smallest βUIP or the largest deviations from UIP in Figures 1a to 1f, a slope

coefficient of −0.41 is obtained from the model. Adding interest smoothing given

_____________________________________________________________________________________91

Figure 3: Average simulated UIP-Beta for different values of a specific modelparameter, recalibrated model "Minimum 1" with smoothing

Figure 3a Share of lagged relative to expected future

inflation in the Phillips curve (απ) Figure 3b

Effect of the output gap on inflation (αy) Figure 3c

Effect of the real exchange rate on the output gap (βq)

Figure 3d

Effect of the real interest rate on the output gap (βρ)

Figure 3e Autocorrelation of the output gap (βy)

Figure 4: Average simulated UIP-Beta for different values of a specific modelparameter, recalibrated model "Minimum 2" with smoothing

Figure 4a Effect of the output gap on inflation (αy)

Figure 4b Effect of the real interest rate on the output

gap (βρ)

92_____________________________________________________________________________________Can Endogenous Monetary Policy Explain the Deviations from UIP

these parameter values lowers it further to −1.36. Finally, repeating the procedurea second time and setting each of the parameters to the value that yields the largest

deviations from UIP in Figures 3a to 3e we obtain an average βUIP of −3.43. Wehave refrained from continuing to search for even larger deviations from UIP as it

is clear that large and negative slope coefficients in the standard UIP test can be

obtained from the model. Instead we proceed to investigating why and how certain

sets of parameter values create large deviations from UIP.

Table 2: Deviations from UIP for four sets of parameter valuesParameters smoothing Average βUIP std(βUIP ) % negativeSvensson No 0.85 0.13 0.0%Minimum 1 No -0.41 0.31 89.4%Minimum 1 Yes -1.36 0.36 99.9%Minimum 2 Yes -3.43 0.93 100.0%

The "minimum 1" parameters are found by setting one parameter at a time to thevalue that yields the largest deviations from UIP. The "minimum 2" parameters arefound by repeating this procedure a second time given interest rate smoothing.

The effect of increasing or decreasing a particular parameter is not necessarily

unique across all parameterization but it is generally the case that larger deviations

fromUIP emerge for (i) high autocorrelation of the risk premium, γϕ, (ii) low relative

weight on lagged inflation in Phillips Curve, απ, (iii) large effect of the output

gap on inflation, αy, (iv) high interest rate sensitivity of output, βρ, and (v) low

autocorrelation of output, βy. A tentative conclusion concerning the mechanisms

behind the deviations from UIP is that parameter values that enhance the effects

of a given change in the interest rate on output and inflation generate low βUIP -

coefficients.

6 Impulse response functions

Why does the Svensson model of endogenous monetary policy in an open economy

generate data on interest rate differentials and realized exchange rate changes that

are inconsistent with UIP for some parameter values? The responses of interest

rates, exchange rate changes, output and inflation to shocks illustrate what happens

in the model. First, there is a shock to the exchange rate risk premium in (12).

Through the modified UIP relationship (11), the nominal and hence real exchange

rate depreciates given the interest rate. Because the weak exchange rate increases

output as well as inflation, the central bank responds by raising the domestic interest

_____________________________________________________________________________________93

rate relative to the foreign. Hence, there will be a depreciation and a positive

interest rate differential in period t as predicted by standard theory. However, in

future periods, the exchange rate appreciates again back towards its equilibrium

but the domestic interest rate remains high or increases further to counteract the

effects of the weak exchange rate on output and inflation. This is where negative

βUIP−coefficients may emerge. The effect is always present in the model but maybe more or less pronounced relative to other movements that are consistent with

UIP depending on the parameter values.

Figures 5a to 5d shows four sets of impulse response functions corresponding

to the four sets of parameter values in Table 2: the Svensson (2000) baseline,

the smallest βUIP−coefficient obtained by combining the parameters yielding thelargest deviations from UIP in Figures 1b to 1f, adding interest smoothing to this

set of parameter values, and combining the parameter values behind the smallest

βUIP−coefficient in Figures 3a to 3e.

Figure 5: Impulse responses from risk premium shock for different modelparameters

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

2 4 6 8 10 12 14 16 18

Exchange Rate Interest Differential

Figure 5a: Responses to Risk Premium Shock, Svensson's Parameters

0.0

0.4

0.8

1.2

1.6

2.0

2 4 6 8 10 12 14 16 18

Exchange Rate Interest Differential

Figure 5b: Resonses to Risk Premium Shock, Minimum 1

0.0

0.5

1.0

1.5

2.0

2.5

3.0

2 4 6 8 10 12 14 16

Exchange Rate Interest Differential

Figure 5c: Responses to Risk Premium Shock, Minimum 1, Smoothing

0

1

2

3

4

2 4 6 8 10 12 14 16

Interest Differential Exchange Rate

Figure 5d: Responses to Risk Premium Shock, Minimum 2

94_____________________________________________________________________________________Can Endogenous Monetary Policy Explain the Deviations from UIP

Negative βUIP−coefficients are obtained from the simultaneous exchange rate

appreciation and higher domestic interest rate. This pattern is always observed

for some periods after a risk premium shock, but the size of the effect relative to

other movements as e.g. new shocks hit the economy varies with the parameter

values. A main finding from the previous section is that interest rate smoothing

increases the deviations from UIP. Comparing Figures 5b and 5c, it is clear that the

exchange rate reacts much more to risk premium shocks with interest rate smooth-

ing than without. This is due to the fact that the interest rate itself reacts less

to shocks with smoothing, which is also visible in these figures. For UIP to hold

in (7), smaller interest movements must be compensated by larger exchange rate

movements. Smoothing strengthens the co-movements of exchange rates and in-

terest rates that are inconsistent with UIP relative to the co-movements that are

consistent with UIP. A second observation from the impulse response functions is

that the effects of shocks on exchange rates and interest rates are much larger in

Figures 5c and 5d than in the Svensson (2000) calibration with smaller values of

the parameters governing the contemporaneous interactions between the variables

and higher autocorrelation of output and inflation. Hence there is always a section

of the response to a risk premium shock where the exchange rate appreciates and

the domestic interest rate exceeds the foreign interest rate. Given the muted in-

terest rate movements induced by smoothing the exchange rate has to react more,

which enhances the co-movements of the two variables that are inconsistent with

UIP relative to those that are consistent with UIP.

7 Decompositions of the deviations from UIP

A second approach to the question why the model sometimes generates large devi-

ations from UIP is indicated by Fama (1984). He decomposes the βUIP−coefficientinto various second moments of the data. The original decomposition uses the vari-

ance of the risk premium relative to the variance of the expected change in the

exchange rate. As discussed in Section 2, a well known conclusion from his calcula-

tions is that a negative relationship between exchange rate changes and interest rate

differentials require that the variance of the risk premium is larger than the variance

of expected exchange rate changes. Meredith (2002) subsequently showed that the

deviation of the βUIP−coefficient from unity formally depends on the product of

the correlation between the risk premium and the interest rate differential and the

variance of the risk premium relative to the variance of the interest rate differen-

_____________________________________________________________________________________95

tial.3 The intuition from Fama is applicable to this decomposition as well since the

variance of expected exchange rate changes is the wedge between the variance of the

risk premium and the variance of the interest rate differential. A main advantage of

using a full scale macro model to analyze the deviations from UIP is that normally

unobservable variables such as the variance of the expected exchange rate change or

the correlation between the risk premium and the interest rate differential can be

obtained endogenously from the model. Hence we are able to dig a little deeper into

the mechanisms behind the negative βUIP -coefficients.

The Meredith (2002) decomposition is derived from the OLS estimator of the

slope coefficient in a regression of exchange rate changes on interest rate differential:

β =cov(y, x)

var(x)=

cov(∆s, (i− i∗))

var(i− i∗). (14)

Using the UIP-relationship and the standard UIP-test in (1) the following ex-

pression can be derived:

βUIP = 1−µρϕ,(i−i∗)

var(ϕ)

var(i− i∗)

¶. (15)

Hence the estimated βUIP -coefficient equals one minus the correlation between

the risk premium and the interest rate differential times the variance of the risk

premium ϕ relative to the variance of the interest rate differential. Since the risk

premium is a part of the interest rate differential in equation (7), ρϕ,(i−i∗) must be

positive but below unity. The variance of the risk premium ϕ is given by γϕ in our

simulations given the unity variance of the true shocks ξϕ whereas the variance of

the interest rate differential is endogenous and depends on parameter values.

Figure 6 shows the βUIP−coefficient, the correlation between the risk premiumand the interest rate differential and the variance of the interest rate differential as

the parameter απ is varied from 0 to 1. απ is the share of backward looking in the

Phillips curve. For this particular combination of parameter values that has been

chosen to illustrate how the decomposition can be used, βUIP varies between -1.35 for

απ=0 to 0.91 for απ=0.95. This strong effect of varying the share of forward looking

expectations in the Phillips curve can be analyzed in terms of the decomposition

in (15). When the Phillips curve is completely forward looking, the correlation

between the risk premium and the interest rate differential is 0.895 and the variance

of the interest rate differential is 0.225. The variance of the risk premium including

autocorrelation is 1.67 for an AR-coefficient of 0.8 in this case. Hence these large

3Meredith (2002) points out that Fama (1984) ignores the correlation between the risk premiumand the interest differential. As far as we can tell, the Meredith decomposition is correct.

96_____________________________________________________________________________________Can Endogenous Monetary Policy Explain the Deviations from UIP

deviations from UIP are created by a combination of a high ρϕ,(i−i∗) and a low

var(i− i∗). As the Phillips curve becomes more and more backward looking, there ismore and more inertia in the inflation rate and the central bank has to pursue a more

and more active monetary policy in order to counteract the effects of a given shock.

Hence the variance of the interest rate increases. For απ = 0.95, inflation is very

persistent and the central bank has to move the interest rate vigorously to achieve

the desired effect. We have a correlation between the risk premium and the interest

rate differential of only 0.20, while the variance of the interest rate differential is

4.48.

Figure 6: Decomposition of the deviations from UIP

-2

-1

0

1

2

3

4

0 0,2 0,4 0,6 0,8

Beta Correlation Var(i-i*)

Decompositions of our four βUIP−coefficients (for the Svensson (2000) parame-ter values, a first round of minimization with and without smoothing and a second

round of minimization with smoothing) are shown in Table 3. The variance of the

risk premium is small in all cases, 1.30 to 1.71 depending on the autocorrelation

coefficient (the variance of the shock is fixed at unity). Empirical estimates of this

unobservable variable are difficult to obtain. The variance of the interest rate differ-

ential is 3.46, 1.12 0.53, and 0.27 for the four different parameterizations, compared

to an estimated value of 2.02.4 However, there is no variation in the foreign interest

rate here since the foreign central bank does not respond optimally to shocks in the

Svensson (2000) model. Since an appreciation of the domestic exchange rate is a

4See the next section for details on the data set used to construct empirical estimates of thesecond moments.

_____________________________________________________________________________________97

depreciation of the foreign exchange rate, there would probably be more variability

in the interest rate differential if the foreign country was modelled as elaborately as

the home country. The correlation between the risk premium and the interest rate

differential is high (0.92-0.96) for the models with large deviations from UIP but only

0.34 in the Svensson parameterization. Again, as this correlation is unobservable

these numbers cannot be compared to actual estimates.

Table 3: Summary of simulation resultsParameters smoothing var(ϕt) Var(i) Corr(ϕt, (i− i∗)) βUIPActual data ? 1.35 2.02 ? -3Svensson No 1.51 3.46 0.34 0.85

Minimum βUIP 1 No 1.71 1.12 0.92 -0.41Minimum βUIP 1 Yes 1.30 0.53 0.96 -1.36Minimum βUIP 2 Yes 1.30 0.27 0.92 -3.43

The "minimum 1" parameters are found by setting one parameter at a time to thevalue that yields the largest deviations from UIP. The "minimum 2" parameters arefound by repeating this procedure a second time given interest rate smoothing.

Hence the decomposition of the deviations fromUIP for the four sets of parameter

values confirms the conclusion from Figure 6. Both a high correlation between the

risk premium and the interest rate differential and a small variance of the interest

rate differential are needed to create large deviations from UIP.

8 Second moments in simulated data

Since negative βUIP−coefficients can be obtained from the model for certain com-

binations of parameter values, each of which falls within a realistic range, it is im-

portant to investigate whether the model behaves reasonably in other dimensions in

these particular cases. In this section we analyze second moments for the generated

data and compare to corresponding estimated moments.

The empirical estimates of the variances and covariances in question are esti-

mated from a standard data set covering four small open economies with a floating

exchange rate regime.5 In Table 4, we can see that the average variances of inflation

rates/output gaps/interest rate differentials are 1.75/1.35/2.02 and the estimated

average correlation between inflation and output gap is 0.23. Given the Svensson

(2000) parameters in the benchmark specification the model produces variances that

5The data are taken from Main Economic Indicators and includes Canada, New Zealand,Sweden, and Switzerland. The sample periods cover the floating exchange rate period of eachcountry.

98_____________________________________________________________________________________Can Endogenous Monetary Policy Explain the Deviations from UIP

are reasonably close to the empirical estimates. The exception is the correlation be-

tween inflation and output gap which is low, only 0.07. This is a feature common

to models of optimal monetary policy. The central bank efficiently counteracts the

effects of demand shocks on inflation and output when they move in the same di-

rection. In the model, observed movements in inflation and output are typically in

opposite directions since monetary policy cannot stabilize both variables simultane-

ously. This implies a low correlation between inflation and output gap in simulated

data from models with optimal monetary policy.

When interest rate smoothing is added to the model the correlation between

inflation and output gap approaches zero. For γϕ set to 0.80, which gives the lowest

βUIP for the recalibrated specification, the inflation variance is 1.09, the output gap

variance is 1.24, and the interest rate variance is 1.12. These numbers are somewhat

lower than corresponding empirical estimates.

For the region where the deviations from UIP are largest, with βUIP below −3,the interest rate variance drops down to around 0.3. The variances of inflation and

output remain somewhat lower than both the benchmark model and empirical esti-

mates, but in contrast to the interest rate variance we do not observe drastic reduc-

tions for the parameterizations associated with negative and large βUIP−coefficients.

Table 4: Second moments in empirical versus generated dataParameters smoothing Var(π) Var(y) Var(i) Corr(π,y)Actual data ? 1.75 1.35 2.02 0.23Svensson No 1.52 1.51 3.46 0.07

Minimum βUIP 1 No 1.09 1.24 1.12 0.00Minimum βUIP 1 Yes 1.06 1.30 0.53 0.00Minimum βUIP 2 Yes 1.03 1.30 0.27 0.00

The "minimum 1" parameters are found by setting one parameter at a time to thevalue that yields the largest deviations from UIP. The "minimum 2" parameters arefound by repeating this procedure a second time given interest rate smoothing.

In general, the parameter specifications with low βUIP have lower variances of

the interest rate differential in particular than both the benchmark specification

and actual data. However, we have hitherto focused solely on finding sets of pa-

rameter values that produce large deviations from UIP. If a reasonable variance of

the interest rate differential is added as a second criterion, it is possible to obtain

negative (although not large) βUIP and at least a unity variance of the interest rate

differential. This can be seen from the decomposition of the deviations from UIP in

(15). Solving this equation for ρϕ,(i−i∗) given var(i− i∗) = 1 it is clear that βUIP is

negative for ρϕ,(i−i∗) >1

var(ϕ)≈ 0.66. Both this correlation and the variance of the

_____________________________________________________________________________________99

interest rate differential emerge endogenously from the model. The highest corre-

lation found given at least a unity variance of the interest rate differential is 0.71,

resulting in a βUIP of −0.07. Equation (15) also shows that the lower bound for theβUIP−coefficient given ρϕ,(i−i∗) = var(i − i∗) = 1 is βUIP = 1 − var(ϕ) or approx-

imately −0.5 given variances of the risk premium from Table 3. Other factors to

bear in mind are that foreign interest rates are constant in the model and empirical

variances of interest rate differentials might be lower than in Table 4 if estimated

using only periods of successful inflation targeting in both countries. Again, this

discussion underlines the crucial importance of the variance of the risk premium for

the resulting deviations from UIP.

9 Conclusions

Tentative evidence indicates that the empirical failure of UIP is confined to short-

term interest rates as existing studies using data on long-term interest rates are less

prone to reject the hypothesis. This paper investigates whether this is a consequence

of the fact that short-term interest rates are used as a monetary policy instrument.

Interest rate and exchange rates are analyzed as two endogenous variables within an

open economy macro model. Both monetary policy and exchange rates respond to

macroeconomic shocks, possibly in ways that create a negative relationship between

interest rate differentials and ex post exchange rate changes. We generate data on

interest rate differentials and exchange rate changes from the Svensson (2000) open

economy model with optimal monetary policy and interest rate smoothing. UIP is

tested on the artificial time series and the resulting βUIP−coefficients are analyzedas the model parameters values are varied within realistic ranges.

In the benchmark case, the βUIP−coefficients that emerge from the Svensson

(2000) model are positive smaller than the unity coefficient expected from UIP.

However, the Svensson (2000) choices of key parameters are small compared to other

estimates. The model can in fact produce βUIP−coefficients below−3 given realisticparameter values. Above all, incorporating interest rate smoothing in the central

bank objective function consistently results in smaller interest rate movements and

larger exchange rate movements in a manner that increases the deviations from UIP.

Other effects working in the same direction are a forward looking Phillips curve, low

autocorrelation of the output gap, large effects of the real interest rate and the

real exchange rate on output, and high autocorrelation of the exchange rate risk

premium. All these mechanisms increase the effect of a given change in the interest

rate on the economy and hence reduce the variance of the interest rate.

100_____________________________________________________________________________________Can Endogenous Monetary Policy Explain the Deviations from UIP

Impulse response functions demonstrate that interest rates respond less and ex-

change rates respond more to risk premium shocks when interest rate smoothing

is included in the objective function. In response to other shocks the relationship

between the two variables is consistent with UIP and the exchange rate moves only

in response to monetary policy. With smoothing, the latter effects are muted as

the central bank avoids large changes in the interest rate. This increases the rela-

tive importance of the co-movements of exchange rates and interest rates that are

inconsistent with UIP. In contrast to previous studies (McCallum (1994), Meredith

and Chinn (1998)) it is not necessary to assume a high variance of the exchange

rate risk premium to obtain a negative relationship between exchange rate changes

and interest rate differentials. Hence the empirical failure of UIP for short-term

interest rates may be due to the fact that short-term interest rates are used as the

monetary policy instrument and both monetary policy and exchange rates respond

endogenously to shocks in a manner that creates the observed phenomenon.

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References

Alexius, Annika, "Uncovered interest parity revisited", Review of International Economics 9, 2001, p. 505-517.

Batini, Nicoletta and Andrew Haldane, "Forward-looking rules for monetary policy", in J. B. Taylor, ed., Monetary Policy Rules, University of Chicago Press, 1999, p. 157-192.

Fama, Eugene, "Forward and Spot Exchange Rates", Journal of Monetary Economics 14, 1984, p. 319-38.

Giovannini, Alberto and Philippe Jorion, "The Time Variation β-coefficients of Risk and Return in the Foreign Exchange and Stock Markets", Journal of Finance 44, 1989, p. 307-25.

Hodrick, Robert, "Risk, Uncertainty and Exchange Rates", Journal of Monetary Economics 23, 1989, p. 433-459.

McCallum, Benneth, "A Reconsideration of the Uncovered Interest Parity Relationship", Journal of Monetary Economics 33, 1994, p. 105-32.

Meese, Richard and Kenneth Rogoff, "Empirical Exchange Rate Models of the Seventies: Do They Fit Out of Sample?", Journal of International Economics 14, 1983, p. 3-24.

Meredith, Guy and Menzie Chinn, "Long-horizon uncovered interest rate parity", NBER Working Paper No. 6797, 1998.

Meredith, Guy, "Uncovered interest parity and the monetary transmission mechanism", in Lavan Mahadeva and Peter Sinclair, eds., Monetary Transmission in Diverse Economies, Cambridge University Press, 2002.

Orphanides, Athanasios and Volker Wieland, "Inflation zone targeting", European Central Bank Working Paper Series No 8, 1999.

Oudiz, Gilles and Jeffrey Sachs, "International policy coordination in dynamic macroeconomic models", in William Buiter and Richard Marston, eds., International Economic Policy Coordination, Cambridge University Press, 1985.

Rotemberg, Julio and Michael Woodford, "An optimization-based econometric framework for the evaluation of monetary policy", NBER Macroeconomics Annual 1997, p. 297-346.

Rudebusch, Glenn and Lars Svensson, "Policy Rules for Inflation Targeting", in John B. Taylor ed., Monetary Policy Rules, University of Chicago Press, 1998.

102_____________________________________________________________________________________Can Endogenous Monetary Policy Explain the Deviations from UIP

Rudebusch, Glenn, "Assessing Nominal Income Rules for Monetary Policy with Model and Data Uncertainty", European Central Bank Working Paper No. 14, 2000.

De Santis, Giorgio and Bruno Gerard, "International Asset Pricing and Portfolio Diversification with Time-Varying Risk", Journal of Finance 52, 1997, p. 1881-1912.

De Santis, Giorgio and Bruno Gerard, "How Big Is the Premium for Currency Risk?", Journal of Financial Economics 49, 1998, p. 375-412.

Smets, Frank, "What horizon for price stability", ECB Working Paper No. 24, 2000.

Svensson Lars E. O., "Inflation forecast targeting: Implementing and monitoring inflation targets", European Economic Review 41, 1997, p. 1111-1146.

Svensson, Lars E. O., "Open-Economy Inflation Targeting," Journal of International Economics 50, 2000, p. 155-183.

Woodford, Michael "Control of the public debt: A requirement for price stability", NBER Working Paper No. 5684, 1996.

Woodford, Michael "Optimal Interest-Rate Smoothing", Review of Economic Studies 70, 2003, p. 861-886.

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Essay 4

Analyzing Unexpected Monetary Policy

1 Introduction Only unexpected monetary policy should affect longer market interest rates and economic activity. This makes it interesting to study when and how the market shifts from incorrect expectations of the next policy move to correctly anticipating the next action of the Federal Reserve, as this transition defines the unexpected interest rate changes that we are interested in. Understanding at what point in time the market typically anticipates Fed policy is helpful both for economists analyzing the transmission mechanisms of monetary policy and for policy makers who want to understand the market reactions to their actions and announcements.

This paper extends the simple expectation error analysis, used as descriptive statistics in for instance Hamilton (2007), to investigate how far in advance of a Federal Open Market Committee (FOMC) meeting the market participants typically anticipate the upcoming policy move. More specifically, expectation errors are aggregated across meetings to study how the accuracy of the expectations changes as the forecasting horizon is extended to up to two months before a scheduled FOMC meeting. The average size of the expectation errors as a function of the forecast horizon shows how the market participants improve their expectations by accumulating new information as the next FOMC meeting is approaching. Two months prior to a meeting the average absolute expectation error is 16 basis points, which is considerable given the typical interest rate change of 25 basis points and an average absolute change of 14 basis points. The average absolute expectation error falls to 10 basis points at the one month horizon. Hence a large part of the information about the upcoming monetary policy move is accumulated during the last month before the policy meeting.

I also calculate the share of all meeting expectations that can be considered correct, defined as the expectation being within 3 basis points of the actual policy outcome. It turns out that 10% of the meetings are fully anticipated 40 trading days ahead of the meeting. This share of meetings is still only 20% at 20 trading days, but gradually increases to 70% for the day before a meeting. The market is better able to predict the outcome of meetings when the FOMC decides to not change the target rate than the outcome of meetings that resulted in a change in the target rate, as the mean absolute expectation errors are about twice as large in the latter case.

The approach for studying unexpected monetary policy presented in this paper can also be used to measure the effect of Federal Reserve transparency, by for instance comparing how well and quickly the market understands the Fed intentions in different time periods. For forecast horizons between 15 and 40 trading days the share of fully anticipated FOMC meetings was four times higher during the period 2000-2006 than

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during 1994-1999, which for a large part can be attributed to improvements in Fed policy transparency.

This paper makes use of the available daily observations of market expectations on the target rate, instead of just observing expectation errors on a monthly frequency. Previous evidence regarding the timing of short term market expectations has focused on either one-day expectations, or expectations on a monthly basis. Krueger and Kuttner (1996) evaluate the funds rate futures as a measure of expectations, and conclude that the futures rate based estimate of the expectations follows the basic axioms of rational expectations. However, at the time of their study the change of announcement procedures after the FOMC meetings were still new, and data was limited. Kuttner (2001) later investigates how one-day policy surprises (the unexpected change of the target rate) affects market interest rates. Unfortunately however, he only includes the FOMC meetings where target changes are instigated, which excludes the events where the target is unexpectedly unchanged. The data shows some large unexpected changes in the target rate, but the focus of the paper does not concern the size of these expectation errors, and therefore this issue is not further analyzed. Poole and Rasche (2000) make a thorough analysis of market expectations derived from futures rates. First, they find that the increased Fed transparency from 1994 has lead to smaller errors in the market expectations. Second, they identify large changes in the futures rate, as these changes represent some kind of major expectations adjustment, and find that most of these changes are due to the arrival of macroeconomic news. Third, as a case study, they point out some different expectations scenarios and display how expectations evolved before a few specific policy meetings. They do not do any extensive empirical analysis of how expectations typically adjust before FOMC meetings. In another paper Poole, Rasche and Thornton (2002) examine these different scenarios further, and they find that Fed policy actions are not widely anticipated until just a few days prior to the ‘action’-meeting. This conclusion is reached using case studies of nine individual changes in the target rate.

Evidence about one- or two-month expectation errors are focused on average errors, often as a part of a risk premium study. Representing this category of studies Piazzesi and Swanson (2006) analyze the average bias in expectations and find that there is a significant negative bias (positive excess return) at both one- and two-month horizon. The magnitudes of these average expectation errors are rather small, with 3 and 6 basis points respectively. No results are reported regarding the spread, or the absolute size, of the errors at these horizons. Hamilton (2007) also explores daily changes in policy expectations derived from the near-term Fed funds futures rates. However, this paper focuses on the pricing of the futures contracts and not much on the expectations

108_____________________________________________________________________________________Analyzing Unexpected Monetary Policy

about monetary policy meetings. Some interesting results are worth mentioning though. From the descriptive statistics we learn that at the one-month horizon the average absolute expectation error is about 7 basis points and for the two-month horizon the corresponding size of the expectation errors is 13 basis points. Adolfson et.al. (2005) is a study that plots average expectation errors and RMSE of different interest rate forecasts against forecast horizon for Swedish data, but they use quarterly data, while this paper is concerned with horizons shorter than two months.

In the light of the previous studies, this study contributes with a new twist to analyzing how well and how quickly the market participants can anticipate the monetary policy moves by the Fed.

The outline of the paper is as follows. In section 2 I describe how to use the funds rate futures rate as a measure of market expectations, and section 3 describes the data material. Section 4 presents and evaluates the empirical results. Section 5 concludes the study.

2 Measuring Market Expectations It is typically difficult to measure expectations as they are not directly observable (Kjellberg, 2006). However, for expectations on the federal funds rate target there is an appealing method for extracting market expectations by using the market traded funds rate futures contracts, traded at the Chicago Board of Trade (CBOT). The use of these contracts as measures of expectations were popularised by for instance Krueger and Kuttner (1996), Söderström (2001), and Kuttner (2001). These futures contracts are settled for the average of the federal funds rate for a specific month.1 The futures rate can be seen as a risk-neutral measure of the expectation on the average federal funds rate for the settlement month. To derive the probability based expectation, i.e. the actual expected value, we would typically have to address the issue of a risk premium. Estimates of the risk premium have been made by for instance Piazzesi and Swanson (2006), and they find large risk premiums for futures rates with several months to maturity. However, the size of the risk premium for one- and two-month expectations seems small, typically in the region of 2-5 basis points at the most.2 The same type of pattern is found by Sack (2004). Hamilton (2007) makes a strong case for negligible

1 For more information about theses futures contracts I refer to Kuttner (2001), or the webpage of CBOT (www.cbot.com). 2 They also find that this risk premium depends on macroeconomic factors, and therefore it seems that changes in this risk premium only occurs over a business cycle frequency.

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risk premiums for futures contracts of up to 3 months to maturity, disputing the results from Piazzesi and Swanson (2006). By allowing innovations in the futures rate to deviate from two of the standard assumptions, normality and i.i.d., he shows that the bias of the futures rate is much smaller and no longer significant. According to Hamilton this is due to a larger probability for negative outliers, making the assumption about normality incorrect.3

As the futures rate might include a highly persistent (or constant) risk premium, albeit small for the horizons considered, it is wise to study changes in the futures rate, rather than the rate value itself. This way the only risk premium that could distort the expectations estimate is any term premium component, i.e. the difference in premium between the forecast occasion and the FOMC meeting. Other than that I do not try to adjust for any risk premium as evidence suggest it is relatively small for the short forecast horizons analysed here, but also because our knowledge about adjusting for such a premium is not good enough.4 This is in line with many other studies deriving short-term expectations from Fed funds futures (see for instance: Poole and Rasche, 2000; Kuttner, 2001; Bernanke and Kuttner, 2005).

By comparing the change in the futures rate when the decision of a FOMC meeting is announced we get an estimate of how surprised the market was with the decision. If the Fed increases the target rate unexpectedly, the futures rate must also increase; otherwise there will be arbitrage opportunities as the underlying asset (the average federal funds rate) increases unexpectedly.

Because the futures rate is based on the average federal funds rate it is not straightforward to interpret the change in the spot futures rate. Presume that the FOMC meeting took place in the middle of the month, then only half of the days that month have a higher interest rate target. The average federal funds rate for that month would only increase by half of the target increase. The same reasoning applies to the change in the futures rate. If the futures rate increases with 10 basis points after the meeting, it approximately reflects an unexpected change in the target rate by 20 basis points. The equation for calculating the unexpected change in the target rate, u

x iτ~Δ , at the meeting

announcement day τ , is

( xsss

sux ff

mm

i −−−

=Δ τττ τ ,,~ )

, (1)

3 In combination with relatively small samples this could cause the significant biases found by Piazzesi and Swanson (2006). 4 As an illustration of the many ways one can try to model the risk premium, and how disparate the results can be, see Durham (2003).

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where is the number of days in the spot-month s, and fs is the daily futures rate for

the spot month. The forecast horizon is altered by changing x. This method of deriving the unexpected change in the target rate is described further in Kuttner (2001).

sm

An alternative way to derive the unexpected change in the target rate is to study the changes in the one month futures rate, i.e. changes in the futures contract that is written with the next month’s average federal funds rate as the underlying asset. A change in the target rate this month should change the path of the federal funds rate for both the current month, and for the upcoming months. Hence, by assuming that the change in the one month futures rate reflects the change in the whole expected path, we can simply take the change in the one month futures rate as the unexpected change of target this month,

xss

ux ffi −++ −=Δ τττ ,1,1~ . (2)

This way of deriving market expectations is used in for instance Poole and Rasche (2000).

The two techniques for deriving the unexpected have different properties, good and bad. Using the spot futures rate ensures that the expectations relate to the studied meeting and month. On the other hand, it suffers from some computational disadvantages for meetings taking place late in the month, where small and irrelevant changes (noise) in the futures rate could be mistaken for big unexpected changes in the target rate. Using the one month futures rate is less complex from a computational aspect, but could include expectations on the next month (meeting) that distorts the estimates of expectations about the current meeting.

As the purpose of this paper is to study how the market expectations change as the next Federal Open Market Committee (FOMC) meeting comes closer, I will vary the forecast horizon of the expectations between 1 to 40 trading days. If the next FOMC meeting is at τ this means that I derive the expectations for τ -1 to τ -40, where the timeline is in CBOT trading days.

As the normal interval between FOMC meetings is about six weeks, i.e. 30 trading days, there will often be another meeting between the day of the expectation and the meeting at time τ . This is a problem for the first method, which uses the spot futures rate, as it implicitly assumes that no change in the target rate happens between the day of the expectation and time τ . The consequence of such an overlap is a distorted measure of the market expectations. Because of this, I choose to rely on the second method and use the one month futures rate when calculating the unexpected change in the Fed target rate.

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3 Data The futures rate data has been supplied by Hansson & Partners AB, and covers the period from 1994 to 2006. Data is available from 1989, but before 1994 there are problems with using the futures rate method to derive market expectations. The most important problem is that before 1994 the FOMC changed the target rate without announcing it, and often between scheduled meetings. This makes it difficult to decide when the market realized that a change had occurred, which also makes it difficult to measure the unexpected component with any accuracy. Therefore I exclude pre-1994 data in this study.

The data is given in futures contract prices, and those are quoted as 100 minus the nominal percentage futures rate. The futures rate data obtained covers all contracts with up to three months to maturity. For a few observations a particular contract has a missing price quote. In that situation I have extrapolated between the previous and the next value, to get a plausible price quote.

Data concerning FOMC meetings, and the federal funds rate target, have been collected from the Board of Governors of the Federal Reserve System website. There are 104 scheduled meetings during the sample period, plus five unscheduled meetings. The unscheduled meetings are not of interest to this study as they, by definition, only can be expected a few days in advance. During 1994 to 2006 there were 30 positive changes in the target rate, 15 negative, and 59 where the target rate was unchanged.5 Details concerning the timing of the FOMC meeting announcements are described by Kuttner (2001) and Poole and Rasche (2000).

4 Expectation Formation as a Function of Forecast Horizon To get an idea about how well the market has predicted the outcome of FOMC meetings at different forecast horizons we can study the expectation errors, i.e. the unexpected change in the Fed target rate. Theoretically, it would seem plausible that the average absolute size of the expectation error decreased as the scheduled meeting approaches. This is a consequence of the basic rational expectations axioms of orthogonality and iterated expectations, where an increase of the information set implies more correct expectations.

5 The unscheduled meetings led to one positive change in the target rate, and four negative changes.

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We can also speculate that at longer forecast horizons, where there is another meeting scheduled before the meeting of interest, the average errors are likely to be higher. If there is an unexpected change at the in-between-meeting it could alter the whole expected path of the target rate and cause the unexpected change at the meeting of interest to be large.6 By studying the expectations data in more detail we learn more about both qualitative and quantitative aspects of the market’s short term predictions. 4.1 Market Expectations on Scheduled FOMC Meetings The target rate expectation errors for different forecast horizons are conveniently illustrated by plotting a line for each FOMC meeting. Each line describes how the expectation error for a certain meeting changes with horizon. In Figure 1 I plot the expectation error for all 104 scheduled meetings during 1994 to 2006. The error values are centred around zero, and seem to be more spread out as the forecast horizon increases.

Figure 1 Expectation errors across different horizons for scheduled FOMC meetings,

1994-2006

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Each line represents a FOMC meeting and shows how large the market expectation errors are for different forecast horizons. The forecast horizon is given in trading days, i.e. one week is typically 5 trading days. The expectation errors are measured in basis points. The sample includes all 104 scheduled meetings from 1994 to 2006.

6 On the other hand, an unexpected change at the in-between-meeting could just be unexpected in timing. For instance, if we at the 1st of January expect a 25 basis point change at the February meeting, but it is realized already at the scheduled meeting in January. This would not increase the expectation error when measuring expectations with the one month futures rate (in this case the March contract).

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Figure 2a-c depicts the descriptive statistics of expectation errors in graph form. As the Figure 2a shows, the average expectation errors are close to zero for the shorter horizons. For horizons up to 20 trading days the point estimate is between zero and -2.5 basis points. The 95% confidence bound include zero for horizons shorter than 25 trading days. For longer horizons the average expectation errors are significantly negative, with averages between -2.5 and -5 basis points. These estimates are in line with what Piazzesi and Swanson (2006) finds for the bias of one- and two-month futures rates.

Figure 2

Descriptive statistics for expectation errors, scheduled FOMC meetings

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The descriptive statistics of the expectation errors are expressed in basis points. The forecast horizon is given in trading days, i.e. one week is typically 5 trading days. The sample includes all 104 scheduled meetings from 1994 to 2006. The confidence interval for the average error is based on the regular standard errors, while the confidence interval for MAE is based on bootstrapped standard errors.

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Note that the significant negative deviations for the longer horizons seem to be driven by the large negative expectation errors from the meetings 2001.7 This year the Fed aggressively, and unexpectedly, lowered the target rate due to an abrupt economic downturn in the US, followed by the 9-11 terror attacks. With this in mind, the overall interpretation of the average expectation errors is that there is no bias, or at least only a very small bias, in the average expectation errors for forecast horizons up to two months. This is in line with research results from Krueger and Kuttner (1996), and Gürkaynak et.al. (2002).

An appropriate measure for the typical size of the expectation errors is the Mean Absolute Error (MAE).8 Using MAE we see in Figure 2b that the average error size is about 3 basis points at the one-day horizon, and then increases with the forecast horizon. At 40 trading days it is 16 basis points, i.e. corresponding to a substantial amount of a standard 25 basis points change of the Fed target. In fact, the average absolute change in the actual federal funds target rate is 14 basis points, further indicating that the error size is considerable at the two month horizon. A typical expectation at a 2-month horizon is therefore as inaccurate as the unconditional mean of the scheduled meeting target rate changes. The positive relation between typical error size and forecast horizon looks almost linear, and is likely to reflect the continuous arrival of new information to the market, improving the accuracy of the expectations. The approximate slope of this relation is on average a third of a basis point for every trading day, which is giving us a hint of how much information per day that the market on average accumulates. The standard deviation of the expectation errors, depicted in Figure 2c, shows a similar behaviour across horizons as the MAE-plot does.9

Taking the absolute value of a bell shaped distribution that is roughly centred around zero gives a distribution that is skewed. With this in mind it can be preferred to study the median absolute error. In Figure 3 both the MAE and the median absolute error are plotted for comparison. The distribution of the absolute expectation errors are definitely skewed as we can see the MAE is considerably higher than the median absolute error. The median error size at the 40-day horizon is 9 basis points, indicating that the typical size of the expectation errors are not quite as high as the MAE tells us. However, the high MAE implies that there are a few meetings that were difficult for the market to anticipate.

7 Excluding the eight meetings during 2001from our sample gives a confidence interval that includes zero for all horizons. 8 The MAE is the average absolute value of the expectation errors. 9 Standard deviation plots are also highly similar to plots of the Root Mean Squared Error (RMSE), not showed here.

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Figure 3 Comparing the mean and the median of the absolute

expectation errors

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The descriptive statistics of the expectation errors are expressed in basis points. The forecast horizon is given in trading days, i.e. one week is typically 5 trading days. The sample includes all 104 scheduled meetings from 1994 to 2006.

In Figure 4 I compare the MAE of the market expectations with the MAE of the naive prediction to expect no change from the day of the forecast to the meeting of interest.10 The naive prediction MAE is here considered an upper bound for the accuracy of market expectations as the sophisticated market expectations should outperform (or at least perform equally with) the naive prediction at any horizon.11 As Figure 4 shows, the MAE of the market expectations is considerably lower for all horizons. For horizons between 20 to 40 trading days the MAE for market expectations is approximately half the size of the MAE of the naive expectations. For shorter forecast horizons the market expectations improve dramatically and at the one-day horizon the MAE is about 20% of the size of the naive expectation errors.

10 Note that the MAE of the naive prediction is the same as the average change in the target rate at different horizons. 11 It should be noted that the naive prediction has a possibility to have really high accuracy during periods of Fed inactivity.

116_____________________________________________________________________________________Analyzing Unexpected Monetary Policy

Figure 4 Mean absolute expectation error – market vs. naive expectations

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The mean absolute errors (MAE) of the expectations are expressed in basis points. The naive expectation is that the federal funds rate target will remain unchanged from the prevailing level. The market expectations are derived from the federal funds futures rate. The forecast horizon is given in trading days, i.e. one week is typically 5 trading days. The sample includes all 104 scheduled meetings from 1994 to 2006.

To be able to shed some light on the question about when the market participants starts to anticipate the upcoming FOMC decisions we can define full anticipation as the expected target rate being less than 3 basis points from the ex post outcome. In Figure 5 I plot the fraction of meetings during 1994 to 2006 where the market had anticipated the outcome, and kept that expectation up until the meeting day. This fraction is plotted against the forecast horizon to let us get an understanding for at what horizon the majority of the meetings have started to be anticipated. At 40 trading days before a meeting less than 10% of the meeting outcomes were anticipated by the market participants, indicating that at this horizon the market cannot properly judge the situation very accurately. But from between 30 and 35 trading days more and more meeting decisions have been anticipated, and this gradually increases as the forecast horizon gets shorter. For five- to ten-day horizons about half of the policy decisions were correctly anticipated; 70% of the decisions were anticipated at the day before the meeting.

The dotted line in Figure 5 is showing the fraction of all meetings that had market expectations within 3 basis points at a specific horizon, but did not necessarily have the same accuracy at the shorter horizons, i.e. sometimes the market changed the expected target rate to a value that is not classified as full anticipation. This fraction is typically

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10-20 percentage points higher than the fraction of meetings where the accurate expectation is maintained all the way until the meeting.12

Figure 5 Fraction of FOMC meeting decisions that were anticipated

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The solid line describes the fraction of all sampled meetings where the market expectation were within 3 basis points from the ex post target rate outcome for a specific horizon and up until the meeting. The dotted line reflects the fraction of meetings where the market expectation is within 3 basis points for the specific forecast horizon. The forecast horizon is given in trading days, i.e. one week is typically 5 trading days. The sample includes all 104 scheduled meetings from 1994 to 2006.

These methods of analysing the day-to-day changes in the market expectations reveals that they are fairly accurate in the very short term, i.e. 1-5 days, with more than 50% of the meetings being fully anticipated, and the average size of the expectation errors being approximately 3 basis points or less. With longer forecast horizons the quality of the expectations deteriorates gradually. At a 40 trading days horizon less than 10% of the meetings were fully anticipated and the typical size of the expectation errors was 16 basis points. The quantitative estimates of the expectation errors are difficult to evaluate, especially as we cannot detect any sudden breaks at any particular forecast horizon. It seems the accuracy is highly dependent on the forecast horizon with gradual improvements of the expectations, which is in line with a continuous flow of new information and rational expectations.

12 By construction the two lines in Figure 4 must converge on the 1-day horizon.

118_____________________________________________________________________________________Analyzing Unexpected Monetary Policy

4.2 Excluding Overlaps When the full sample of scheduled FOMC meetings is analyzed the longer horizon expectations can include an overlap with the previous FOMC meeting. Meetings are typically taking place with about a six week interval, i.e. approximately around 30 trading days apart, so with sufficiently long forecast horizons it is likely that there is a meeting in between the day of the ‘forecast’ and the meeting being ‘forecasted’. But there are also a few unscheduled meetings that can occur just a few days before a regular meeting. As any FOMC meeting is potentially a substantial source for new information about the policy decision on the upcoming meetings, these overlaps are interesting for this type of analysis.

If there is an unscheduled meeting in between the time of the expectation and the scheduled meeting of interest, it is very likely to cause a substantial expectation error as the expected path of the target rate is altered. Excluding expectations that overlap with unscheduled meetings does indeed change the average magnitudes of the expectation errors, but the qualitative results remain the same. Excluding the unscheduled meetings is a form of outlier exclusion and serves to find the ‘normal’ quantitative estimates of the expectation errors. The estimates in Figure 6a-c, where overlaps with unexpected meetings have been excluded, are therefore more correct in reflecting the properties of the typical errors in target rate expectations. Figure 6a reveals that the average expectation error is typically as small as 1 to 2 basis points, across forecast horizons of one day up to 40 days. The 95% confidence band includes zero as a probable value for the majority of the considered forecast horizons. In Figure 6b we see that the MAE increases with forecast horizon, from 3 basis points at the one-day horizon, to 12 basis points at the 40-day horizon. The 40-day MAE is 4 basis points lower after we have excluded overlaps with the five unscheduled meetings. Figure 6c describes a similar pattern for the standard deviation. In both Figure 6b and 6c the plot is fairly linear, except between the 28- to 31-day horizons where a slight increase of the slope can be discerned. This interval is common between scheduled meetings (about six weeks, i.e. about 30 trading days), implying that even a scheduled meeting might bring new information to the market that affects the next meeting.

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Figure 6 Descriptive statistics for expectation errors,

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Forecast Horizon in Days

c) Standard Deviation of Expectations Errors

The descriptive statistics of the expectation errors are expressed in basis points. The forecast horizon is given in trading days, i.e. one week is typically 5 trading days. The sample includes all 104 scheduled meetings from 1994 to 2006, however, for longer horizons the sample size decreases as overlaps with previous meetings are excluded. At the 40-day horizon the sample consists of 98 observations.

The conclusion from observing the higher error magnitudes in the full sample Figures 2a-c, compared to the overlap adjusted estimates in Figures 6a-c, must be that an unscheduled meeting changes the whole expected path of the target rate, and therefore makes the previous expectations about the next scheduled meeting less accurate. However, it turns out that excluding scheduled overlaps as well is not changing the properties of the expectation errors much (not shown here).

120_____________________________________________________________________________________Analyzing Unexpected Monetary Policy

4.3 FOMC Meetings with and without Action The sample of scheduled FOMC meetings includes both meetings where it is decided to change the target rate and meetings where it is decided to leave the target unchanged. If we split the sample into these two categories an interesting result regarding the average expectation errors is revealed. In Figure 7a-b I plot the expectation errors of the two categories separately.

Figure 7 Expectation errors across different horizons for scheduled FOMC meetings

a) Expectation errors for ’Action’-meetings

0 5 10 15 20 25 30 35 40

-100

-50

0

50

100

Forecast Horizon in Days

Exp

ecta

tions

Erro

r in

Bas

is P

oint

s

b) Expectation errors for ’No Action’-meetings

0 5 10 15 20 25 30 35 40

-100

-50

0

50

100

Forecast Horizon in Days

Exp

ecta

tions

Erro

r in

Bas

is P

oint

s

Each line represents a FOMC meeting and shows how large the market expectation errors are for different forecast horizons. The forecast horizon is given in trading days, i.e. one week is typically 5 trading days. The expectation errors are measured in basis points. Note that the errors of FOMC meetings with negative changes have reversed signs to improve interpretability. The sample includes all 104 scheduled meetings from 1994 to 2006, with 45 observations in a) and 59 in b).

_____________________________________________________________________________________121

The average errors for ‘action’-meetings, i.e. for when the sample only includes meetings where it was decided to change the target rate, are shown in Figure 8a. Note that this average is taking into account that the meaning of a positive or negative expectation error is different when the actual change in the target rate is negative.13 I have reversed the sign on all expectation errors for meetings with negative changes in the target rate to improve the interpretability of the simple average of expectation errors. If we compare this diagram with the full sample counterpart in Figure 2a, we see that the average expectation errors are now significantly positive for all horizons. This implies that the market on a consistent basis underestimates the actual outcome of the meetings where the FOMC decides to change the target rate. The point estimates in the action sample are all higher, and even though the 95% confidence interval is wider (due to fewer observations) it never includes zero.14 The relation between the modified average error and the forecast horizon is positive. The point estimate magnitudes range from about 3 basis points at the one-day horizon to 20 basis points at the 40-day horizon. Both the MAE and the standard deviation of the expectation errors, in Figure 8b-c, are quantitatively higher compared to the full sample estimates in Figure 2b-c. This tells us that the absolute size of the errors of ‘action’-meeting expectations are typically substantially bigger compared to the full sample MAE and standard deviations shown in Figure 2b-c.

13 For instance, with a positive change in the target rate, a positive expectation error implies that the market has underestimated the size of the change. With a negative change of the target rate, a positive error is an overestimation of the actual change. 14 This is robust to excluding the 2001 observations, as well as excluding overlap observations.

122_____________________________________________________________________________________Analyzing Unexpected Monetary Policy

Figure 8 Descriptive statistics of expectation errors for ‘Action’-meetings

0 5 10 15 20 25 30 35 40-30

-20

-10

0

10

20

30 a) Average Expectations Error

0 5 10 15 20 25 30 35 400

10

20

30

Exp

ecta

tions

Erro

r in

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is P

oint

s b) Mean Absolute Expectations Error

0 5 10 15 20 25 30 35 400

10

20

30

Forecast Horizon in Days

c) Standard Deviation of Expectations Errors

The descriptive statistics of the expectation errors are expressed in basis points. The forecast horizon is given in trading days, i.e. one week is typically 5 trading days. The sample includes all 45 scheduled meetings from 1994 to 2006 where the federal funds rate target was changed.

The average expectation errors for meetings where the FOMC decided to keep the target rate unchanged can be viewed in Figure 9a. The average errors are rather small, within 5 basis points of zero for all studied horizons. For most forecast horizons the confidence interval includes zero. MAE and standard deviation, shown in Figure 9b-c, indicate that the spread of the expectation errors for this sub-sample is lower than for the sub-sample with only ‘action’-meetings. The MAE is slightly less than 2 basis points at the one-day horizon, and then increases with the forecast horizon, to 10 basis points at the 40-day horizon.

_____________________________________________________________________________________123

Figure 9 Descriptive statistics of expectation errors for ‘No Action’-meetings

0 5 10 15 20 25 30 35 40-30

-20

-10

0

10

20

30 a) Average Expectations Error

0 5 10 15 20 25 30 35 400

10

20

30

Exp

ecta

tions

Erro

r in

Bas

is P

oint

s b) Mean Absolute Expectations Error

0 5 10 15 20 25 30 35 400

10

20

30

Forecast Horizon in Days

c) Standard Deviation of Expectations Errors

The descriptive statistics of the expectation errors are expressed in basis points. The forecast horizon is given in trading days, i.e. one week is typically 5 trading days. The sample includes all 59 scheduled meetings from 1994 to 2006 where the federal funds rate target was not changed.

The most important difference between ‘action’-meetings and ‘no action’-meetings is the positive and significant average expectation errors for the ‘action’-meetings. Before the ‘no action’-meetings the expectations seem to be more accurate, and also converge towards full anticipation faster. In Figure 10 we see the fractions of FOMC decisions that were anticipated for ‘action’- and ‘no action’-meetings respectively. The outcomes of the ‘action’-meetings are more seldom anticipated; at the 40-day horizon about 5% of these meetings are anticipated, compared to more than 10% for the ‘no action’-meetings. At the one-day horizon only half of the meeting outcomes were fully anticipated for ‘action’-meetings, while almost 90 % of the ‘no action’-meetings were

124_____________________________________________________________________________________Analyzing Unexpected Monetary Policy

fully anticipated. The market insights, where the fraction of meetings seems to increase, appear to arrive around specific points in time: 20-day, ten-day, and one- to three-day horizons.

Figure 10

Fraction of FOMC meetings anticipated ‘Action’- vs. ‘No Action’-meetings

0 5 10 15 20 25 30 35 400

10

20

30

40

50

60

70

80

90

100

Forecast Horizon in Days

Frac

tion

of M

eetin

gs (%

)

Accurate Expectations (+/- 3bp) - No Action MeetingAccurate Expectations (+/- 3bp) - Action Meeting

The two samples include the 59 scheduled FOMC meetings where the target rate was unchanged (No Action Meetings) and the 45 scheduled meetings where the target rate was altered (Action Meetings). The forecast horizon is given in trading days, i.e. one week is typically 5 trading days. The sample includes all 104 scheduled meetings from 1994 to 2006.

5 Measuring Impact of Improved Transparency The approach to analysing expectations taken in this paper is also useful for measuring the impact of improved central bank transparency. In order to illustrate how this works I study the difference in market anticipation capabilities between 1994-1999 and 2000-2006. Previous research has confirmed that Fed transparency was much improved after 1994 and lead to a better market understanding of Fed policy (Lange, Sack and Whitesell, 2003; Poole and Rasche, 2000; Swanson, 2004). For instance, Swanson (2004) finds that both FOMC announcement surprises, and ex ante uncertainty about future funds rate changes, are lower for the post-1994 period compared to the pre-1994 period. He also concludes that, as the predictions of macroeconomic variables have not

_____________________________________________________________________________________125

improved since 1994, the improvement of market expectations about Fed policy is likely to mostly be due to increased Fed transparency. Due to the lack of quality data before 1994, in particular the problem of identifying the timing of the policy moves, I choose to not compare pre-1994 and post-1994 market anticipation. However, Hamilton (2007) presents empirical estimates that indicate that the market’s understanding of Fed policy also has improved since year 2000. Along the same line of reasoning as Swanson, Hamilton concludes that this recent improvement in market understanding of policy should be attributed to further improvements of the Fed policy communication.15 During 1999 the FOMC started to present a statement after each FOMC meeting of the committee’s view of the likely direction of future policy moves. From year 2000 the statement was modified to be a balance-of-risk assessment, assessing the goals of future price stability and economic growth.16 These statements are likely to help the financial market participants to make better policy forecasts, and could explain the empirical observation of Hamilton (2007). In a short policy related article Carlson, et.al. (2006) compare the average absolute expectation errors for the pre-1994 era and the post-1999 era, as a comparison of low versus high transparency periods. The plot indicates a huge improvement with half the size of absolute errors for the recent period.17

However, Ehrmann and Fratzscher (2005) find somewhat contradicting results, claiming that the market ability to anticipate the FOMC meeting outcomes, within a week before the meetings, has not changed since 1999. However, they also find that the market reach this level of anticipation earlier, i.e. the level of anticipation the last few days before a meeting have not changed, but this level of anticipation is reached earlier than before.18 The method used in Figure 4 is very useful when studying these claims more in detail and it makes a fine example of how this approach can be used to analyze transparency effects. In Figure 11 I plot the fractions of fully anticipated scheduled meeting decisions between 1994 and 1999, compared to the time period 2000 to 2006. It is quite obvious that there are quite substantial differences, across all horizons, contrary to the conclusion of Ehrmann and Fratzscher (2005).

15 According to Hamilton (2007), these differences cannot exclusively be attributed to more predictable policy actions lately, but are most likely due to improved central bank transparency. 16 For more information about these statement changes I refer to Ehrmann and Fratzscher (2005). 17 Carlson et.al. seem to use the Kuttner (2001) method of calculating expectation errors, and the absolute expectation errors do not decrease monotonically with forecast horizon, but rather in a more jagged fashion. 18 As opposed to Hamilton (2007) and this paper, Ehrmann and Fratzscher (2005) measure expectations using surveys conducted by Reuters and Money Market Services.

126_____________________________________________________________________________________Analyzing Unexpected Monetary Policy

Figure 11 Fraction of FOMC meeting decisions that were anticipated

1994-1999 vs. 2000-2006

0 5 10 15 20 25 30 35 400

10

20

30

40

50

60

70

80

90

100

Forecast Horizon in Days

Frac

tion

of M

eetin

gs (%

)Accurate Expectations (+/- 3bp) - 1994 to 1999Accurate Expectations (+/- 3bp) - 2000 to 2006

The two samples include the 45 scheduled FOMC meetings from 1994 to 1999 and the 59 scheduled meetings from 2000 to 2006. The forecast horizon is given in trading days, i.e. one week is typically 5 trading days.

Before we can speculate that these improvements are due to greater transparency we need to study whether the policy actions themselves have become more predictable or not.19 We also need to consider if the two time periods appears to have any apparent difference in major shocks to the economy (Poole, 2005; Carlson et.al., 2006). Regardless of the quality of the market knowledge about Fed policy we cannot expect the policy responses to such exogenous shocks to be anticipated. In Table 1 I present a breakdown of the types of Fed policy moves that took place during the two different sub-samples and they show that if anything the period after 1999 the Fed policy seems at least as active and volatile as the period 1994-1999. The share of ‘no change’-meetings have actually decreased since 1999 and as these can be argued to be easier to predict (Ehrmann and Fratzscher, 2005) it appears as the FOMC policy decisions have not been remarkably easier to predict after 1999. The share of scheduled meetings that lead to target rate changes larger than 50 basis points was 8.9% for 1994-1999 and 11.9% for 2000-2006, indicating no dramatic difference in large policy moves that could be due to major economic shocks. Hence, the substantial changes we see in the

19 Improved transparency can be defined as the short-run predictability of policy outcomes. See for instance Meirelles-Aurelio (2005).

_____________________________________________________________________________________127

market ability to anticipate Fed policy is likely to be a result of improved Fed transparency.

Table 1

FOMC meetings and federal funds rate target changes Target Rate Change 1994-2006 1994-1999 2000-2006

+75bp 1 (1,0%) 1 (2,2%) 0 (0,0%)

+50bp 4 (3,8%) 3 (6,7%) 1 (1,7%)

+25bp 25 (24,0%) 5 (11,1%) 20 (33,9%)

No Change 59 (56,7%) 31 (68,9%) 28 (47,5%)

-25bp 9 (8,7%) 5 (11,1%) 4 (6,8%)

-50bp 6 (5,8%) 0 (0,0%) 6 (10,2%)

-75bp 0 (0,0%) 0 (0,0%) 0 (0,0%)

The table shows the number of FOMC meetings that decided to do a specific change in the Federal funds rate target. The corresponding percentage share of all meetings in the sample is displayed in parenthesis.

From Figure 11 it seems that the market has really improved the ability to forecast the upcoming policy outcomes, as the fractions of fully anticipated FOMC meetings are much larger for the later sub-period.20 In the early sub-sample we can see that virtually no policy moves were anticipated at horizons longer than about 15 days. During 2000-2006 the fraction of anticipated meetings is four times the fraction in the earlier period for horizons above 15 trading days. In the earlier period only 10% of the policy meetings were fully anticipated at the 15-day horizon, while the corresponding figure for the later period of the sample was more than 45%. The fraction of anticipated meetings at the 1-day horizon is 80% for 2000-2006, and 60% for 1994-1999.

I find that the market participants have started to have a correct expectation of meeting outcomes much earlier during the period 2000 to 2006, compared to the period 1994 to 1999. One can conclude that during 1994-1999 expectations improved mostly during the last month before the FOMC meeting, while during 2000-2006 expectations improve during the last two months. This is further evidence to the existing knowledge about the impact of central bank transparency, supporting the Hamilton (2007) hypothesis of improved market expectations during the 2000s due to changes in Fed policy communications.

20 Alternatively, we could claim that the Fed policy has become more predictable.

128_____________________________________________________________________________________Analyzing Unexpected Monetary Policy

6 Conclusions

Only unexpected changes in the Fed target rate should have any impact on the long market interest rates and economic activity. This paper shows how average expectation errors as a function of the forecasting horizon can be constructed and used to analyze issues like when these monetary policy surprises typically occur. The market expectations are derived from changes in the Fed funds futures rate. A possible critique against this kind of interpretation of the findings is that part of the estimated changes in expectations could be changes in a possible futures contract risk premium instead of expectation changes. However, such a premium would probably only constitute of a couple of basis points for these short horizons. As Hamilton (2007) points out, previous estimates of futures rate risk premiums are imprecise and he concludes that for horizons up to three months the risk premiums are likely to be insignificant and smaller than estimated in for instance Piazzessi and Swansson (2006). Hence, as the techniques for estimating any risk premium in the Fed funds futures rate are still imprecise, and the results regarding the risk premiums are somewhat contradicting, I refrain from adjusting for a possible risk premium as it could distort the expectation estimate just as much as it could correct it.

Like previous studies have found, this study confirms that one day before an FOMC meeting the market often anticipates the policy announcement from the upcoming meeting. By extending the forecast horizon we can see that the market participants improve their prediction gradually as the meeting gets closer in time, with the average absolute expectation error falling from 16 basis points two months prior to a scheduled meeting to 10 basis points at the monthly horizon. This is a substantial error as the typical average absolute change in the Federal funds target rate is 14 basis points. At the two month horizon not even 10% of the FOMC meetings are fully anticipated by the market participants.

I compare the quantitative sizes of the market expectation errors with the errors from a naive prediction model, and find that for horizons longer than 20 trading days the market MAE is consistently about 50% of the MAE for the naive prediction. This indicates that the market expectations are fairly accurate for these forecast horizons. During the last 20 trading days before a meeting, the accuracy of the market expectations improve dramatically compared to the naive predictions.

It is evident that inaccuracy of the expectations, as measured by MAE or standard deviation of the errors, increases with forecast horizon. This supports the basic axioms of rational expectations, where the information set is smaller for longer forecast horizons and therefore leads to less accurate expectations about the future.

_____________________________________________________________________________________129

I also find that unscheduled in-between meetings, taking place after the forecast but before the forecasted meeting, seem to create higher expectation errors for the following scheduled meeting. Unscheduled meetings alter the future path of the target rate and bring new information to the market. Another observation is that the meetings that decide to change the target rate are more difficult to predict accurately than meetings that decide to keep the target rate unchanged. The absolute average of the expectation errors for meetings where the target rate is changed is twice the size of the corresponding figure for ‘no change’-meetings. We also see that the errors in expectations for ‘action’-meetings are due to underestimating the target rate change. This might seem natural, but it is well worth noting that the market participants appear to have a bias towards expecting ‘no change’ to be a probable alternative for the FOMC.

A remarkable improvement in expectation accuracy can be observed from 2000, compared to the period 1994-1999. After 1999 the shares of fully anticipated meetings for horizons between one and two months were at least four times the corresponding shares during 1994-1999. The market ability to predict Fed policy has also changed for the better for horizons shorter than a month, where for instance the fraction of meetings anticipated at the one-day horizon increased from about 60% to 80%. The improvements are substantial and support the claim of Hamilton (2007) that the Fed transparency has improved during this period, having a positive impact on market expectations.

The type of analysis used in this paper can be useful as it yields additional insights into how market expectations adapt and change before policy meetings. The timing of the monetary policy surprises can be pinned down and a new way of measuring transparency is provided.

130_____________________________________________________________________________________Analyzing Unexpected Monetary Policy

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